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

A087183 Partition numbers of the form 3*k.

Original entry on oeis.org

3, 15, 30, 42, 135, 231, 297, 627, 792, 1002, 1575, 2436, 5604, 8349, 10143, 14883, 31185, 37338, 44583, 63261, 105558, 147273, 239943, 281589, 329931, 614154, 1121505, 1505499, 3087735, 4087968, 4697205, 8118264, 15796476, 44108109
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 23 2003

Keywords

Comments

The numbers m such that 3 divides A000041(m) are given in A083214. Klarreich writes: no one has proved whether there are infinitely many partition numbers divisible by 3, although it is known that there are infinitely many partition numbers divisible by 2. - Jonathan Vos Post, Jul 31 2008
Intersection of A008585 and A000041. - Reinhard Zumkeller, Nov 03 2009

References

  • Erica Klarreich, Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes, Science News, Jun 18 2005.

Links

Crossrefs

Cf. A000041, A008585, A068907, A052001, A052003, A079978, A083214, A087180, A087184, A087185, A167392, A213365.

Programs

Formula

A079978(a(n))*A167392(a(n)) = 1. - Reinhard Zumkeller, Nov 03 2009
a(n) = 3*A213365(n). - Omar E. Pol, May 08 2013
a(n) = A000041(A083214(n)). - Amiram Eldar, May 22 2025

A213179 Numbers k such that 2*k is a partition number.

Original entry on oeis.org

1, 11, 15, 21, 28, 88, 245, 396, 501, 979, 1218, 1505, 1859, 2802, 3421, 6155, 18669, 26587, 44567, 52779, 62377, 102113, 225638, 307077, 357610, 415910, 650078, 870815, 1006279, 1161760, 2043984, 3544750, 4059132, 6066082, 6924325, 7898238, 13271830
Offset: 1

Views

Author

Omar E. Pol, Feb 27 2013

Keywords

Examples

			11 is in the sequence because 2*11 = 22 and 22 is a partition number: p(8) = A000041(8) = 22.

Crossrefs

Cf. A000041, A052001, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225323.

Programs

  • Mathematica
    Select[PartitionsP[Range@200]/2, IntegerQ] (* Giovanni Resta, May 05 2013 *)

Formula

a(n) = A052001(n)/2.

A216258 Numbers n such that 4n is a partition number.

Original entry on oeis.org

14, 44, 198, 609, 1401, 112819, 178805, 207955, 325039, 580880, 1021992, 1772375, 2029566, 3033041, 3949119, 6635915, 23167430, 29528576, 37549534, 47642323, 96069084, 120875711, 135486560, 190250539, 212844157, 297227062, 331927519, 461087390, 572830228
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			14 is in the sequence because 4*14 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Crossrefs

Cf. A000041, A213179, A213365, A217725, A217726, A222175, A222178, A222179, A225317, A225323, A225324.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 4] == 0 &]/4 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225324(j)/4.

Extensions

a(9)-a(29) from R. J. Mathar, May 05 2013

A217725 Numbers n such that 5n is a partition number.

Original entry on oeis.org

1, 3, 6, 27, 77, 98, 251, 315, 602, 913, 2462, 5203, 6237, 15035, 34705, 77231, 143044, 166364, 224301, 348326, 464704, 617547, 710869, 939441, 1417900, 2769730, 4101251, 5308732, 9999185, 18533944, 26646186, 33845975, 54249790, 60960273, 108389248
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			3 is in the sequence because 5*3 = 15 and 15 is a partition number: p(7) = A000041(7) = 15.

Crossrefs

Cf. A000041, A213179, A213365, A216258, A217726, A222175, A222178, A222179, A225317, A225323, A225325.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 5] == 0 &]/5 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225325(j)/5.

Extensions

a(9)-a(35) from R. J. Mathar, May 05 2013

A217726 Numbers n such that 6n is a partition number.

Original entry on oeis.org

5, 7, 132, 167, 406, 934, 6223, 17593, 102359, 681328, 1353044, 2632746, 22205155, 64046056, 473656750, 527187892, 805878645, 1224438252, 3073382220, 5064778663, 7510104097, 17906359911, 23799832655, 114159565156, 303450183442, 557560997283, 662166504898
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			5 is in the sequence because 6*5 = 30 and 30 is a partition number: p(9) = A000041(9) = 30.

Crossrefs

Cf. A000041, A213179, A213365, A216258, A217725, A222175, A222178, A222179, A225317, A225323, A225326.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 6] == 0 &]/6 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225326(j)/6.

Extensions

a(9)-a(27) from T. D. Noe, May 05 2013

A222175 Numbers n such that 7n is a partition number.

Original entry on oeis.org

1, 6, 8, 11, 33, 55, 70, 225, 348, 430, 1449, 3091, 4455, 5334, 6369, 17822, 21039, 40227, 47133, 55165, 64468, 160215, 441105, 1159752, 1327013, 2929465, 3334067, 7142275, 16873472, 19032990, 38749850, 86737678, 97129029, 189672868, 405991500, 451875336, 852077072, 1756048833, 2152268305, 3558408287, 4341238854, 7098041203
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			6 is in the sequence because 7*6 = 42 and 42 is a partition number: p(10) = A000041(10) = 42.

Crossrefs

Cf. A000041, A213179, A213365, A216258, A217725, A217726, A222178, A222179, A225317, A225323, A225327.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 7] == 0 &]/7 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225327(j)/7.

Extensions

a(9)-a(42) from R. J. Mathar, May 05 2013

A222178 Numbers n such that 8n is a partition number.

Original entry on oeis.org

7, 22, 99, 290440, 510996, 1014783, 11583715, 14764288, 18774767, 48034542, 67743280, 148613531, 230543695, 286415114, 395390919, 543884825, 671414425, 745567438, 918328689, 1251947710, 1387205627, 2083836151, 2305036665, 4628419400, 7544584160, 37673100256
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			7 is in the sequence because 8*7 = 56 and 56 is a partition number: p(11) = A000041(11) = 56.

Crossrefs

Cf. A000041, A213179, A213365, A216258, A217725, A217726, A222175, A222179, A225317, A225323, A225358.

Programs

  • Mathematica
    Select[PartitionsP[Range@200]/8, IntegerQ] (* Giovanni Resta, May 05 2013 *)

Formula

a(j) = A225358(j)/8.

Extensions

a(5)-a(26) from Giovanni Resta, May 05 2013

A222179 Numbers n such that 9n is a partition number.

Original entry on oeis.org

15, 33, 88, 175, 1127, 3465, 7029, 36659, 1755164, 4900901, 537252430, 816292168, 1365815759, 2048921480, 11937573274, 14434878293, 17435497255, 27826547235, 169697066625, 371707331522, 405119159125, 800760189610, 23737435535625, 86561181062463, 100528900924040
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			15 is in the sequence because 9*15 = 135 and 135 is a partition number: p(14) = A000041(14) = 135.

Crossrefs

Cf. A000041, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A225317, A225323, A225360.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 9] == 0 &]/9 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225360(j)/9.

Extensions

a(6)-a(25) from R. J. Mathar, May 05 2013

A225317 Numbers k such that 10k is a partition number.

Original entry on oeis.org

3, 49, 301, 1231, 71522, 83182, 174163, 232352, 708950, 1384865, 2654366, 9266972, 13323093, 27124895, 54194624, 184434956, 284194050, 435107860, 483527187, 537131540, 1001558168, 1844029332, 3702735520, 6035667328, 14279899593, 27476861713, 39712507475, 43515769783, 47671585729, 62584675312
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Comments

Partition numbers ending in 10 divided by 10.

Examples

			3 is in the sequence because 10*3 = 30 and 30 is a partition number: p(9) = A000041(9) = 30.

Crossrefs

Cf. A000041, A127544, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225323.

Programs

  • Mathematica
    Select[PartitionsP[Range[300]], Mod[#, 10] == 0 &]/10 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A127544(j)/10.

A225323 Numbers n such that 11n is a partition number.

Original entry on oeis.org

1, 2, 7, 16, 21, 27, 35, 57, 72, 178, 338, 415, 622, 759, 1353, 1967, 2365, 2835, 4053, 4834, 5751, 15775, 18566, 21813, 25599, 35105, 47893, 65020, 75620, 101955, 118196, 158330, 490253, 644500, 738024, 1102924, 1636757, 1864205, 2121679, 2413060, 2742487, 3535243, 8424520, 10737664, 13654376, 27709215, 31120519
Offset: 1

Views

Author

Omar E. Pol, May 05 2013

Keywords

Examples

			2 is in the sequence because 11*2 = 22 and 22 is a partition number: p(8) = A000041(8) = 22.

Crossrefs

Cf. A000041, A027827, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225361.

Programs

  • Mathematica
    Select[PartitionsP[Range[100]], Mod[#, 11] == 0 &]/11 (* T. D. Noe, May 05 2013 *)

Formula

a(j) = A225361(j)/11.

Extensions

a(11)-a(47) from R. J. Mathar, May 05 2013
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.