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 1-9 of 9 results.

A322691 Five-column table read by rows: Primitive distinct 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
Offset: 1

Views

Author

Jud McCranie, Dec 30 2018

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. This sequence has primitive terms only. If k is relatively prime to all of the terms in a primitive quintuple, then multiplying the terms in that quintuple by k gives another solution - see A322681.
From David A. Corneth, Feb 15 2019: (Start)
Some numbers occur in more than one quintuple, for example 1773744050 is in the quintuples [1579877800, 1652932372, 1653851276, 1663815260, 1773744050] and [1652932372, 1653851276, 1663815260, 1773744050, 1774581050].
The 4693 distinct terms in the first 5000 terms have only 111 distinct prime factors, the largest being 22751. All of these primes differ 1 from a 29-smooth number. (End)
From David A. Corneth, Feb 17 2019: (Start)
A quintuple (e1, e2, e3, e4, e5) is valid and primitive if and only if
1. The elements are in increasing order.
2. Every element e of the quintuple has the same value for phi(e), sigma(e) and tau(e).
3. For every number k between e1 and e5 that's not in the quintuple, at least one of the following statements is false: phi(e1) = phi(k), sigma(e1) = sigma(k), tau(e1) = tau(k).
4. Let g be gcd(e1, e2, e3, e4, e5). Then for every d|g, (e1/d, e2/d, e3/d, e4/d, e5/d) is not a valid quintuple. Therefore, (e1, e2, e3, e4, e5) is primitive. (End)

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.

Links

Crossrefs

Cf. A134922, A322681, A322688, A322689, A322690, A322692, A322693, A322694, A322695, A322696, A322697, A306430.

A322687 Eleven-column table read by rows: 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, Jan 16 2019

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. Primitive solutions are in A322697.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322682, A322683, A322684, A322685, A322686.

A322679 Three-column table read by rows: 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, 315240, 335610, 354090
Offset: 1

Views

Author

Jud McCranie, Jan 15 2019

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. Primitive triples are in A322689.

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.

Crossrefs

Cf. A134922, A322689, A322678, A322680, A322681, A322682, A322683, A322684, A322685, A322686, A322687.

A322680 Four-column table read by rows: 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, 6595560, 6917064, 6960840, 7818690
Offset: 1

Views

Author

Jud McCranie, Jan 16 2019

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. Primitive solutions are in A322690.

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.

Crossrefs

Cf. A134922, A322689, A322678, A322679, A322681, A322682, A322683, A322684, A322685, A322686, A322687.

A322682 Six-column table read by rows: 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, Jan 16 2019

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. Primitive solutions are in A322692.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322683, A322684, A322685, A322686, A322687.

A322683 Seven-column table read by rows: 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, Jan 16 2019

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. Primitive solutions are in A322693.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322682, A322684, A322685, A322686, A322687.

A322684 Eight-column table read by rows: 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
Offset: 1

Views

Author

Jud McCranie, Jan 16 2019

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. Primitive solutions are in A322694.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322682, A322683, A322685, A322686, A322687.

A322685 Nine-column table read by rows: 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
Offset: 1

Views

Author

Jud McCranie, Jan 16 2019

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. The primitive solutions are in A322995.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322682, A322683, A322684, A322686, A322687.

A322686 Ten-column table read by rows: 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, Jan 16 2019

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. Primitive solutions are in A322696.

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.

Crossrefs

Cf. A134922, A322692, A322679, A322680, A322681, A322682, A322683, A322684, A322685, A322687.
Showing 1-9 of 9 results.

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