cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

A322692 Six-column table read by rows: Primitive distinct sextuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

98422632, 98724000, 99373500, 100693920, 101356380, 111298770, 98724000, 99373500, 100693920, 101356380, 111298770, 114002850, 152611020, 152891400, 161014380, 162770850, 171652650, 171733650, 173949984, 185635044, 187420296, 195265356, 195856836, 210450786
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive sextuples, ordered so that (A) a(6i-5) < a(6i-4) < ... < a(6i) for i > 0, and (B) a(6i+1) < a(6i+7) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive sextuple, then multiplying the terms in that sextuple by k gives another solution - see A322682.

Examples

			98422632, 98724000, 99373500, 100693920, 101356380, and 111298770 have the same value of phi (24883200), sigma (341228160), and tau (192), so these six numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322682, A322688, A322689, A322690, A322691, A322693, A322694, A322695, A322696, A322697.

A322689 Three-column table read by rows: Primitive distinct triples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

63048, 67122, 70818, 106120, 115938, 122322, 121352, 122120, 137170, 133920, 140448, 141372, 206112, 207468, 218892, 226632, 242730, 254562, 227304, 228000, 229500, 247968, 260832, 262548, 273824, 290812, 290852, 282720, 284580, 298452, 302560, 319396, 342550, 330144, 332316, 364914
Offset: 1

Views

Author

Jud McCranie, Dec 23 2018

Keywords

Comments

The terms are consecutive triples, ordered so that (A) a(3i-2) < a(3i-1) < a(3i), and (B) a(3i-2) < a(3j-2) for i < j. This sequence has primitive terms only. If k is relatively prime to all of the terms in a primitive triple, then multiplying the terms in that triple by k gives another solution - see A322679.

Examples

			phi(63048) = phi(67122) = phi(70818) = 20160, sigma(63048) = sigma(67122) = sigma(70818) = 164160, tau(63048) = tau(67122) = tau(70818) = 32, so 63048, 67122, and 70818 are in the sequence.

Links

Crossrefs

Cf. A134922, A322679, A322688, A322690, A322691, A322692, A322693, A322694, A322695, A322696, A322697.

A322690 Four-column table read by rows: Primitive distinct quadruples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

1167320, 1197912, 1275318, 1345542, 3502548, 3536232, 3684252, 3695412, 4846520, 4980792, 5302638, 5594622, 5196000, 5299680, 5857830, 6000150, 5276448, 5568672, 5605308, 5764220, 6115656, 6510834, 6866106, 6869346, 6119520, 6159780, 6586650, 6928350
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive quadruples, ordered so that (A) a(4i-3) < a(4i-2) < a(4i-1) < a(4i) for i > 0, and (B) a(4i+1) < a(4i+5) for i >= 0. This sequence has primitive terms only. If k is relatively prime to all of the terms in a primitive quadruple, then multiplying the terms in that quadruple by k gives another solution - see A322680.

Examples

			1167320, 1197912, 1275318, and 1345542 have the same value of phi (362880), sigma (3283200), and tau (64), so these four numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322680, A322688, A322689, A322691, A322692, A322693, A322694, A322695, A322696, A322697.

A322693 Seven-column table read by rows: Primitive distinct septuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

98422632, 98724000, 99373500, 100693920, 101356380, 111298770, 114002850, 306564000, 312681120, 314675820, 335624850, 345611970, 353938650, 354008850, 378502560, 387919200, 390471300, 399564396, 402010740, 428530050, 428773950, 620451360, 650334048, 650695584, 654615840, 654976476, 661275384, 691042044
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive septuples, ordered so that (A) a(7i-6) < a(7i-5) < ... < a(7i) for i > 0, and (B) a(7i+1) < a(7i+8) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive septuple, then multiplying the terms in that septuple by k gives another solution - see A322683.

Examples

			98422632, 98724000, 99373500, 100693920, 101356380, 111298770, and 114002850 have the same value of phi (24883200), sigma (341228160), and tau (192), so these seven numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322683, A322688, A322689, A322690, A322691, A322692, A322694, A322695, A322696, A322697.

A322694 Eight-column table read by rows: Primitive distinct octuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

1068277140, 1070239800, 1078550760, 1123696860, 1127100660, 1139395950, 1201568550, 1202135550, 2145948000, 2188767840, 2202730740, 2317003260, 2349373950, 2419283790, 2477570550, 2478061950, 2232975640, 2234245720, 2296145112, 2296166952, 2444516118, 2578842354, 2579120742, 2580251718, 2739065760
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive octuples, ordered so that (A) a(8i-7) < a(8i-6) < ... < a(8i) for i > 0, and (B) a(8i+1) < a(8i+9) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive octuple, then multiplying the terms in that octuple by k gives another solution - see A322684.

Examples

			1068277140, 1070239800, 1078550760, 1123696860, 1127100660, 1139395950, 1201568550, 1202135550 have the same value of phi (232243200), sigma (3989744640), and tau (384), so these eight numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322684, A322688, A322689, A322690, A322691, A322692, A322693, A322695, A322696, A322697.

A322696 Ten-column table read by rows: Primitive distinct 10-tuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

5701466232, 5806935288, 5824716000, 5863036500, 5940941280, 5978840580, 5980026420, 6376872150, 6520948434, 6566627430, 5806935288, 5824716000, 5863036500, 5940941280, 5978840580, 5980026420, 6376872150, 6520948434, 6566627430, 6726168150
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive 10-tuples, ordered so that (A) a(10i-9) < a(10i-8) < ... < a(10i) for i > 0, and (B) a(10i+1) < a(10i+11) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive 10-tuple, then multiplying the terms in that 10-tuple by k gives another solution - see A322686.

Examples

			5701466232, 5806935288, 5824716000, 5863036500, 5940941280, 5978840580, 5980026420, 6376872150, 6520948434, and 6566627430 have the same value of phi (1443225600), sigma (20473689600), and tau (384), so these ten numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322686, A322688, A322689, A322690, A322691, A322692, A322693, A322694, A322695, A322697.

A322688 Two-column table read by rows: Primitive distinct pairs that have the same value of phi, sigma, and tau.

Original entry on oeis.org

568, 638, 1824, 1836, 3051, 3219, 4185, 4389, 4960, 5236, 6368, 6764, 7749, 8151, 9184, 9724, 9760, 11050, 11032, 12470, 11176, 12586, 13420, 14350, 15169, 15265, 17376, 19206, 18788, 20150, 23848, 26866, 26355, 27962, 26784, 29260, 28809, 30381, 30199, 30217, 32128, 33128, 32940, 37050, 34144, 36244, 37592, 39795
Offset: 1

Views

Author

Jud McCranie, Dec 31 2018

Keywords

Comments

The terms are consecutive pairs, ordered so that (A) a(2i-1) < a(2i) for i > 0, and (B) a(2i+1) < a(2i+3) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive pair, then multiplying the terms in that pair by k gives another solution - see A134922. In Burton's book (see references), problem 3 in section 7.2 asks the reader to prove a special case for (568,638).

Examples

			phi(568)=phi(638)=280; sigma(568)=sigma(638)=1080; tau(568)=tau(638)=8.

References

  • David Burton, Elementary Number Theory, 4th edition, 1998, section 7.2.

Links

Crossrefs

Cf. A134922, A322687, A322689, A322690, A322691, A322692, A322693, A322694, A322695, A322696, A322696.

A322695 Nine-column table read by rows: Primitive distinct 9-tuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

4337267040, 4548689376, 4577446560, 4578614964, 4606647660, 4607561340, 5024337318, 5056654590, 5059532610, 4343835816, 4344550776, 4467333640, 4467573880, 4583778744, 4584409224, 4879970766, 4880641986, 5149389234, 4775185440, 5003255712, 5007954336, 5036171868, 5039648160, 5040901404, 5072803740
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive 9-tuples, ordered so that (A) a(9i-8) < a(9i-7) < ... < a(9i) for i > 0, and (B) a(9i+1) < a(9i+10) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all the terms in a primitive 9-tuple, then multiplying the terms in that 9-tuple by k gives another solution - see A322685.

Examples

			4337267040, 4548689376, 4577446560, 4578614964, 4606647660, 4607561340, 5024337318, 5056654590, and 5059532610 have the same value of phi (1106472960), sigma (15850598400), and tau (384), so these nine numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322685, A322688, A322689, A322690, A322691, A322692, A322693, A322694, A322696, A322697.

A322697 Eleven-column table read by rows: Primitive distinct 11-tuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

5701466232, 5806935288, 5824716000, 5863036500, 5940941280, 5978840580, 5980026420, 6376872150, 6520948434, 6566627430, 6726168150, 28249479864, 29028683320, 29045194360, 29849886456, 29850170376, 31778709534, 31888948266, 33524950602, 33528569646, 33543272334, 33644878554
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

Keywords

Comments

The terms are consecutive 11-tuples, ordered so that (A) a(11i-10) < a(11i-9) < ... < a(11i) for i > 0, and (B) a(11i+1) < a(11i+12) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive 11-tuple, then multiplying the terms in that 11-tuple by k gives another solution - see A322687.

Examples

			5701466232, 5806935288, 5824716000, 5863036500, 5940941280, 5978840580, 5980026420, 6376872150, 6520948434, 6566627430, and 6726168150 have the same value of phi (1443225600), sigma (20473689600), and tau (384), so these eleven numbers are in the sequence.

Links

Crossrefs

Cf. A134922, A322687, A322688, A322689, A322690, A322691, A322692, A322693, A322694, A322695, A322696.

Extensions

More terms from Jud McCranie, Jan 13 2019

A322681 Five-column table read by rows: Quintuples that have the same value of phi, sigma, and tau.

Original entry on oeis.org

15132960, 15870624, 15966240, 15975036, 16854684, 15175160, 15572856, 16579134, 16629354, 17492046, 17671392, 18346968, 18644448, 20598318, 20608038, 26382240, 27668256, 27843360, 27850284, 28026540, 28020384, 29474016, 29563296, 29667924, 31301556, 30743000, 31130008, 31356440, 34531750, 35220790
Offset: 1

Views

Author

Jud McCranie, Jan 16 2019

Keywords

Comments

The terms are consecutive quintuples, ordered so that (A) a(5i-4) < a(5i-3) < ... < a(5i) for i > 0, and (B) a(5i+1) < a(5i+6) for i >= 0. Primitive terms are in A322691.

Examples

			15132960, 15870624, 15966240, 15975036,and 16854684 have the same value of phi (3870720), sigma (55157760), and tau (192), so these five numbers are in the sequence.

Crossrefs

Cf. A134922, A322689, A322678, A322679, A322680, A322682, A322683, A322684, A322685, A322686, A322687.
Showing 1-10 of 11 results. Next

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