Quadratische Pyramidalzahlen

Einleitung

Eine Quadratische Pyramidalzahl beziffert die Anzahl von Kugeln, mit denen man eine Pyramide quadratischer Grundfläche bauen kann. Die Quadratischen Pyramidalzahl zählt neben den Tetraederzahlen zu den Pyramidalzahlen (Pyramidenzahlen).

Formel

Aus einer natürlichen Zahl n lässt sich nach folgender Formel deren quadratische Pyramidalzahl berechnen:
Formel für eine Quadratische Pyramidalzahl n

Beispiel:

Beispiel einer Berechnung der Quadratische Pyramidalzahl von 5

Inhaltsverzeichnis

 

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Quadratische Pyramidalzahl von 0

Hier finden Sie die quadratische Pyramidalzahl von 0.
Bei einigen Autoren ist die Null keine quadratische Pyramidalzahl, sodass die Zahlenfolge erst mit der Eins beginnt.

p0 = 0

 

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Quadratische Pyramidalzahlen von 1 bis 100

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 1 bis 100.

p1 → p10 p1 = 1p2 = 5p3 = 14p4 = 30p5 = 55p6 = 91p7 = 140p8 = 204p9 = 285p10 = 385
p11 → p20 p11 = 506p12 = 650p13 = 819p14 = 1015p15 = 1240p16 = 1496p17 = 1785p18 = 2109p19 = 2470p20 = 2870
p21 → p30 p21 = 3311p22 = 3795p23 = 4324p24 = 4900p25 = 5525p26 = 6201p27 = 6930p28 = 7714p29 = 8555p30 = 9455
p31 → p40 p31 = 10416p32 = 11440p33 = 12529p34 = 13685p35 = 14910p36 = 16206p37 = 17575p38 = 19019p39 = 20540p40 = 22140
p41 → p50 p41 = 23821p42 = 25585p43 = 27434p44 = 29370p45 = 31395p46 = 33511p47 = 35720p48 = 38024p49 = 40425p50 = 42925
p51 → p60 p51 = 45526p52 = 48230p53 = 51039p54 = 53955p55 = 56980p56 = 60116p57 = 63365p58 = 66729p59 = 70210p60 = 73810
p61 → p70 p61 = 77531p62 = 81375p63 = 85344p64 = 89440p65 = 93665p66 = 98021p67 = 102510p68 = 107134p69 = 111895p70 = 116795
p71 → p80 p71 = 121836p72 = 127020p73 = 132349p74 = 137825p75 = 143450p76 = 149226p77 = 155155p78 = 161239p79 = 167480p80 = 173880
p81 → p90 p81 = 180441p82 = 187165p83 = 194054p84 = 201110p85 = 208335p86 = 215731p87 = 223300p88 = 231044p89 = 238965p90 = 247065
p91 → p100 p91 = 255346p92 = 263810p93 = 272459p94 = 281295p95 = 290320p96 = 299536p97 = 308945p98 = 318549p99 = 328350p100 = 338350

 

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Quadratische Pyramidalzahlen von 101 bis 200

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 101 bis 200.

p101 → p110 p101 = 348551p102 = 358955p103 = 369564p104 = 380380p105 = 391405p106 = 402641p107 = 414090p108 = 425754p109 = 437635p110 = 449735
p111 → p120 p111 = 462056p112 = 474600p113 = 487369p114 = 500365p115 = 513590p116 = 527046p117 = 540735p118 = 554659p119 = 568820p120 = 583220
p121 → p130 p121 = 597861p122 = 612745p123 = 627874p124 = 643250p125 = 658875p126 = 674751p127 = 690880p128 = 707264p129 = 723905p130 = 740805
p131 → p140 p131 = 757966p132 = 775390p133 = 793079p134 = 811035p135 = 829260p136 = 847756p137 = 866525p138 = 885569p139 = 904890p140 = 924490
p141 → p150 p141 = 944371p142 = 964535p143 = 984984p144 = 1005720p145 = 1026745p146 = 1048061p147 = 1069670p148 = 1091574p149 = 1113775p150 = 1136275
p151 → p160 p151 = 1159076p152 = 1182180p153 = 1205589p154 = 1229305p155 = 1253330p156 = 1277666p157 = 1302315p158 = 1327279p159 = 1352560p160 = 1378160
p161 → p170 p161 = 1404081p162 = 1430325p163 = 1456894p164 = 1483790p165 = 1511015p166 = 1538571p167 = 1566460p168 = 1594684p169 = 1623245p170 = 1652145
p171 → p180 p171 = 1681386p172 = 1710970p173 = 1740899p174 = 1771175p175 = 1801800p176 = 1832776p177 = 1864105p178 = 1895789p179 = 1927830p180 = 1960230
p181 → p190 p181 = 1992991p182 = 2026115p183 = 2059604p184 = 2093460p185 = 2127685p186 = 2162281p187 = 2197250p188 = 2232594p189 = 2268315p190 = 2304415
p191 → p200 p191 = 2340896p192 = 2377760p193 = 2415009p194 = 2452645p195 = 2490670p196 = 2529086p197 = 2567895p198 = 2607099p199 = 2646700p200 = 2686700

 

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Quadratische Pyramidalzahlen von 201 bis 300

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 201 bis 300.

p201 → p210 p201 = 2727101p202 = 2767905p203 = 2809114p204 = 2850730p205 = 2892755p206 = 2935191p207 = 2978040p208 = 3021304p209 = 3064985p210 = 3109085
p211 → p220 p211 = 3153606p212 = 3198550p213 = 3243919p214 = 3289715p215 = 3335940p216 = 3382596p217 = 3429685p218 = 3477209p219 = 3525170p220 = 3573570
p221 → p230 p221 = 3622411p222 = 3671695p223 = 3721424p224 = 3771600p225 = 3822225p226 = 3873301p227 = 3924830p228 = 3976814p229 = 4029255p230 = 4082155
p231 → p240 p231 = 4135516p232 = 4189340p233 = 4243629p234 = 4298385p235 = 4353610p236 = 4409306p237 = 4465475p238 = 4522119p239 = 4579240p240 = 4636840
p241 → p250 p241 = 4694921p242 = 4753485p243 = 4812534p244 = 4872070p245 = 4932095p246 = 4992611p247 = 5053620p248 = 5115124p249 = 5177125p250 = 5239625
p251 → p260 p251 = 5302626p252 = 5366130p253 = 5430139p254 = 5494655p255 = 5559680p256 = 5625216p257 = 5691265p258 = 5757829p259 = 5824910p260 = 5892510
p261 → p270 p261 = 5960631p262 = 6029275p263 = 6098444p264 = 6168140p265 = 6238365p266 = 6309121p267 = 6380410p268 = 6452234p269 = 6524595p270 = 6597495
p271 → p280 p271 = 6670936p272 = 6744920p273 = 6819449p274 = 6894525p275 = 6970150p276 = 7046326p277 = 7123055p278 = 7200339p279 = 7278180p280 = 7356580
p281 → p290 p281 = 7435541p282 = 7515065p283 = 7595154p284 = 7675810p285 = 7757035p286 = 7838831p287 = 7921200p288 = 8004144p289 = 8087665p290 = 8171765
p291 → p300 p291 = 8256446p292 = 8341710p293 = 8427559p294 = 8513995p295 = 8601020p296 = 8688636p297 = 8776845p298 = 8865649p299 = 8955050p300 = 9045050

 

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Quadratische Pyramidalzahlen von 301 bis 400

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 301 bis 400.

p301 → p310 p301 = 9135651p302 = 9226855p303 = 9318664p304 = 9411080p305 = 9504105p306 = 9597741p307 = 9691990p308 = 9786854p309 = 9882335p310 = 9978435
p311 → p320 p311 = 10075156p312 = 10172500p313 = 10270469p314 = 10369065p315 = 10468290p316 = 10568146p317 = 10668635p318 = 10769759p319 = 10871520p320 = 10973920
p321 → p330 p321 = 11076961p322 = 11180645p323 = 11284974p324 = 11389950p325 = 11495575p326 = 11601851p327 = 11708780p328 = 11816364p329 = 11924605p330 = 12033505
p331 → p340 p331 = 12143066p332 = 12253290p333 = 12364179p334 = 12475735p335 = 12587960p336 = 12700856p337 = 12814425p338 = 12928669p339 = 13043590p340 = 13159190
p341 → p350 p341 = 13275471p342 = 13392435p343 = 13510084p344 = 13628420p345 = 13747445p346 = 13867161p347 = 13987570p348 = 14108674p349 = 14230475p350 = 14352975
p351 → p360 p351 = 14476176p352 = 14600080p353 = 14724689p354 = 14850005p355 = 14976030p356 = 15102766p357 = 15230215p358 = 15358379p359 = 15487260p360 = 15616860
p361 → p370 p361 = 15747181p362 = 15878225p363 = 16009994p364 = 16142490p365 = 16275715p366 = 16409671p367 = 16544360p368 = 16679784p369 = 16815945p370 = 16952845
p371 → p380 p371 = 17090486p372 = 17228870p373 = 17367999p374 = 17507875p375 = 17648500p376 = 17789876p377 = 17932005p378 = 18074889p379 = 18218530p380 = 18362930
p381 → p390 p381 = 18508091p382 = 18654015p383 = 18800704p384 = 18948160p385 = 19096385p386 = 19245381p387 = 19395150p388 = 19545694p389 = 19697015p390 = 19849115
p391 → p400 p391 = 20001996p392 = 20155660p393 = 20310109p394 = 20465345p395 = 20621370p396 = 20778186p397 = 20935795p398 = 21094199p399 = 21253400p400 = 21413400

 

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Quadratische Pyramidalzahlen von 401 bis 500

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 401 bis 500.

p401 → p410 p401 = 21574201p402 = 21735805p403 = 21898214p404 = 22061430p405 = 22225455p406 = 22390291p407 = 22555940p408 = 22722404p409 = 22889685p410 = 23057785
p411 → p420 p411 = 23226706p412 = 23396450p413 = 23567019p414 = 23738415p415 = 23910640p416 = 24083696p417 = 24257585p418 = 24432309p419 = 24607870p420 = 24784270
p421 → p430 p421 = 24961511p422 = 25139595p423 = 25318524p424 = 25498300p425 = 25678925p426 = 25860401p427 = 26042730p428 = 26225914p429 = 26409955p430 = 26594855
p431 → p440 p431 = 26780616p432 = 26967240p433 = 27154729p434 = 27343085p435 = 27532310p436 = 27722406p437 = 27913375p438 = 28105219p439 = 28297940p440 = 28491540
p441 → p450 p441 = 28686021p442 = 28881385p443 = 29077634p444 = 29274770p445 = 29472795p446 = 29671711p447 = 29871520p448 = 30072224p449 = 30273825p450 = 30476325
p451 → p460 p451 = 30679726p452 = 30884030p453 = 31089239p454 = 31295355p455 = 31502380p456 = 31710316p457 = 31919165p458 = 32128929p459 = 32339610p460 = 32551210
p461 → p470 p461 = 32763731p462 = 32977175p463 = 33191544p464 = 33406840p465 = 33623065p466 = 33840221p467 = 34058310p468 = 34277334p469 = 34497295p470 = 34718195
p471 → p480 p471 = 34940036p472 = 35162820p473 = 35386549p474 = 35611225p475 = 35836850p476 = 36063426p477 = 36290955p478 = 36519439p479 = 36748880p480 = 36979280
p481 → p490 p481 = 37210641p482 = 37442965p483 = 37676254p484 = 37910510p485 = 38145735p486 = 38381931p487 = 38619100p488 = 38857244p489 = 39096365p490 = 39336465
p491 → p500 p491 = 39577546p492 = 39819610p493 = 40062659p494 = 40306695p495 = 40551720p496 = 40797736p497 = 41044745p498 = 41292749p499 = 41541750p500 = 41791750

 

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Quadratische Pyramidalzahlen von 501 bis 600

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 501 bis 600.

p501 → p510 p501 = 42042751p502 = 42294755p503 = 42547764p504 = 42801780p505 = 43056805p506 = 43312841p507 = 43569890p508 = 43827954p509 = 44087035p510 = 44347135
p511 → p520 p511 = 44608256p512 = 44870400p513 = 45133569p514 = 45397765p515 = 45662990p516 = 45929246p517 = 46196535p518 = 46464859p519 = 46734220p520 = 47004620
p521 → p530 p521 = 47276061p522 = 47548545p523 = 47822074p524 = 48096650p525 = 48372275p526 = 48648951p527 = 48926680p528 = 49205464p529 = 49485305p530 = 49766205
p531 → p540 p531 = 50048166p532 = 50331190p533 = 50615279p534 = 50900435p535 = 51186660p536 = 51473956p537 = 51762325p538 = 52051769p539 = 52342290p540 = 52633890
p541 → p550 p541 = 52926571p542 = 53220335p543 = 53515184p544 = 53811120p545 = 54108145p546 = 54406261p547 = 54705470p548 = 55005774p549 = 55307175p550 = 55609675
p551 → p560 p551 = 55913276p552 = 56217980p553 = 56523789p554 = 56830705p555 = 57138730p556 = 57447866p557 = 57758115p558 = 58069479p559 = 58381960p560 = 58695560
p561 → p570 p561 = 59010281p562 = 59326125p563 = 59643094p564 = 59961190p565 = 60280415p566 = 60600771p567 = 60922260p568 = 61244884p569 = 61568645p570 = 61893545
p571 → p580 p571 = 62219586p572 = 62546770p573 = 62875099p574 = 63204575p575 = 63535200p576 = 63866976p577 = 64199905p578 = 64533989p579 = 64869230p580 = 65205630
p581 → p590 p581 = 65543191p582 = 65881915p583 = 66221804p584 = 66562860p585 = 66905085p586 = 67248481p587 = 67593050p588 = 67938794p589 = 68285715p590 = 68633815
p591 → p600 p591 = 68983096p592 = 69333560p593 = 69685209p594 = 70038045p595 = 70392070p596 = 70747286p597 = 71103695p598 = 71461299p599 = 71820100p600 = 72180100

 

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Quadratische Pyramidalzahlen von 601 bis 700

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 601 bis 700.

p601 → p610 p601 = 72541301p602 = 72903705p603 = 73267314p604 = 73632130p605 = 73998155p606 = 74365391p607 = 74733840p608 = 75103504p609 = 75474385p610 = 75846485
p611 → p620 p611 = 76219806p612 = 76594350p613 = 76970119p614 = 77347115p615 = 77725340p616 = 78104796p617 = 78485485p618 = 78867409p619 = 79250570p620 = 79634970
p621 → p630 p621 = 80020611p622 = 80407495p623 = 80795624p624 = 81185000p625 = 81575625p626 = 81967501p627 = 82360630p628 = 82755014p629 = 83150655p630 = 83547555
p631 → p640 p631 = 83945716p632 = 84345140p633 = 84745829p634 = 85147785p635 = 85551010p636 = 85955506p637 = 86361275p638 = 86768319p639 = 87176640p640 = 87586240
p641 → p650 p641 = 87997121p642 = 88409285p643 = 88822734p644 = 89237470p645 = 89653495p646 = 90070811p647 = 90489420p648 = 90909324p649 = 91330525p650 = 91753025
p651 → p660 p651 = 92176826p652 = 92601930p653 = 93028339p654 = 93456055p655 = 93885080p656 = 94315416p657 = 94747065p658 = 95180029p659 = 95614310p660 = 96049910
p661 → p670 p661 = 96486831p662 = 96925075p663 = 97364644p664 = 97805540p665 = 98247765p666 = 98691321p667 = 99136210p668 = 99582434p669 = 100029995p670 = 100478895
p671 → p680 p671 = 100929136p672 = 101380720p673 = 101833649p674 = 102287925p675 = 102743550p676 = 103200526p677 = 103658855p678 = 104118539p679 = 104579580p680 = 105041980
p681 → p690 p681 = 105505741p682 = 105970865p683 = 106437354p684 = 106905210p685 = 107374435p686 = 107845031p687 = 108317000p688 = 108790344p689 = 109265065p690 = 109741165
p691 → p700 p691 = 110218646p692 = 110697510p693 = 111177759p694 = 111659395p695 = 112142420p696 = 112626836p697 = 113112645p698 = 113599849p699 = 114088450p700 = 114578450

 

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Quadratische Pyramidalzahlen von 701 bis 800

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 701 bis 800.

p701 → p710 p701 = 115069851p702 = 115562655p703 = 116056864p704 = 116552480p705 = 117049505p706 = 117547941p707 = 118047790p708 = 118549054p709 = 119051735p710 = 119555835
p711 → p720 p711 = 120061356p712 = 120568300p713 = 121076669p714 = 121586465p715 = 122097690p716 = 122610346p717 = 123124435p718 = 123639959p719 = 124156920p720 = 124675320
p721 → p730 p721 = 125195161p722 = 125716445p723 = 126239174p724 = 126763350p725 = 127288975p726 = 127816051p727 = 128344580p728 = 128874564p729 = 129406005p730 = 129938905
p731 → p740 p731 = 130473266p732 = 131009090p733 = 131546379p734 = 132085135p735 = 132625360p736 = 133167056p737 = 133710225p738 = 134254869p739 = 134800990p740 = 135348590
p741 → p750 p741 = 135897671p742 = 136448235p743 = 137000284p744 = 137553820p745 = 138108845p746 = 138665361p747 = 139223370p748 = 139782874p749 = 140343875p750 = 140906375
p751 → p760 p751 = 141470376p752 = 142035880p753 = 142602889p754 = 143171405p755 = 143741430p756 = 144312966p757 = 144886015p758 = 145460579p759 = 146036660p760 = 146614260
p761 → p770 p761 = 147193381p762 = 147774025p763 = 148356194p764 = 148939890p765 = 149525115p766 = 150111871p767 = 150700160p768 = 151289984p769 = 151881345p770 = 152474245
p771 → p780 p771 = 153068686p772 = 153664670p773 = 154262199p774 = 154861275p775 = 155461900p776 = 156064076p777 = 156667805p778 = 157273089p779 = 157879930p780 = 158488330
p781 → p790 p781 = 159098291p782 = 159709815p783 = 160322904p784 = 160937560p785 = 161553785p786 = 162171581p787 = 162790950p788 = 163411894p789 = 164034415p790 = 164658515
p791 → p800 p791 = 165284196p792 = 165911460p793 = 166540309p794 = 167170745p795 = 167802770p796 = 168436386p797 = 169071595p798 = 169708399p799 = 170346800p800 = 170986800

 

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Quadratische Pyramidalzahlen von 801 bis 900

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 801 bis 900.

p801 → p810 p801 = 171628401p802 = 172271605p803 = 172916414p804 = 173562830p805 = 174210855p806 = 174860491p807 = 175511740p808 = 176164604p809 = 176819085p810 = 177475185
p811 → p820 p811 = 178132906p812 = 178792250p813 = 179453219p814 = 180115815p815 = 180780040p816 = 181445896p817 = 182113385p818 = 182782509p819 = 183453270p820 = 184125670
p821 → p830 p821 = 184799711p822 = 185475395p823 = 186152724p824 = 186831700p825 = 187512325p826 = 188194601p827 = 188878530p828 = 189564114p829 = 190251355p830 = 190940255
p831 → p840 p831 = 191630816p832 = 192323040p833 = 193016929p834 = 193712485p835 = 194409710p836 = 195108606p837 = 195809175p838 = 196511419p839 = 197215340p840 = 197920940
p841 → p850 p841 = 198628221p842 = 199337185p843 = 200047834p844 = 200760170p845 = 201474195p846 = 202189911p847 = 202907320p848 = 203626424p849 = 204347225p850 = 205069725
p851 → p860 p851 = 205793926p852 = 206519830p853 = 207247439p854 = 207976755p855 = 208707780p856 = 209440516p857 = 210174965p858 = 210911129p859 = 211649010p860 = 212388610
p861 → p870 p861 = 213129931p862 = 213872975p863 = 214617744p864 = 215364240p865 = 216112465p866 = 216862421p867 = 217614110p868 = 218367534p869 = 219122695p870 = 219879595
p871 → p880 p871 = 220638236p872 = 221398620p873 = 222160749p874 = 222924625p875 = 223690250p876 = 224457626p877 = 225226755p878 = 225997639p879 = 226770280p880 = 227544680
p881 → p890 p881 = 228320841p882 = 229098765p883 = 229878454p884 = 230659910p885 = 231443135p886 = 232228131p887 = 233014900p888 = 233803444p889 = 234593765p890 = 235385865
p891 → p900 p891 = 236179746p892 = 236975410p893 = 237772859p894 = 238572095p895 = 239373120p896 = 240175936p897 = 240980545p898 = 241786949p899 = 242595150p900 = 243405150

 

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Quadratische Pyramidalzahlen von 901 bis 1000

Hier finden Sie eine Liste der quadratischen Pyramidalzahlen von 901 bis 1000.

p901 → p910 p901 = 244216951p902 = 245030555p903 = 245845964p904 = 246663180p905 = 247482205p906 = 248303041p907 = 249125690p908 = 249950154p909 = 250776435p910 = 251604535
p911 → p920 p911 = 252434456p912 = 253266200p913 = 254099769p914 = 254935165p915 = 255772390p916 = 256611446p917 = 257452335p918 = 258295059p919 = 259139620p920 = 259986020
p921 → p930 p921 = 260834261p922 = 261684345p923 = 262536274p924 = 263390050p925 = 264245675p926 = 265103151p927 = 265962480p928 = 266823664p929 = 267686705p930 = 268551605
p931 → p940 p931 = 269418366p932 = 270286990p933 = 271157479p934 = 272029835p935 = 272904060p936 = 273780156p937 = 274658125p938 = 275537969p939 = 276419690p940 = 277303290
p941 → p950 p941 = 278188771p942 = 279076135p943 = 279965384p944 = 280856520p945 = 281749545p946 = 282644461p947 = 283541270p948 = 284439974p949 = 285340575p950 = 286243075
p951 → p960 p951 = 287147476p952 = 288053780p953 = 288961989p954 = 289872105p955 = 290784130p956 = 291698066p957 = 292613915p958 = 293531679p959 = 294451360p960 = 295372960
p961 → p970 p961 = 296296481p962 = 297221925p963 = 298149294p964 = 299078590p965 = 300009815p966 = 300942971p967 = 301878060p968 = 302815084p969 = 303754045p970 = 304694945
p971 → p980 p971 = 305637786p972 = 306582570p973 = 307529299p974 = 308477975p975 = 309428600p976 = 310381176p977 = 311335705p978 = 312292189p979 = 313250630p980 = 314211030
p981 → p990 p981 = 315173391p982 = 316137715p983 = 317104004p984 = 318072260p985 = 319042485p986 = 320014681p987 = 320988850p988 = 321964994p989 = 322943115p990 = 323923215
p991 → p1000 p991 = 324905296p992 = 325889360p993 = 326875409p994 = 327863445p995 = 328853470p996 = 329845486p997 = 330839495p998 = 331835499p999 = 332833500p1000 = 333833500
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