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 31 results. Next

A056848 Numbers k that divide the number of partitions of k into distinct parts (A000009).

Original entry on oeis.org

1, 10, 16, 65, 160, 180, 366, 406, 896, 1436, 3904, 5464, 6312, 7168, 12558, 17957, 36960, 48097, 48256, 61952, 88646, 94400, 107340, 112240, 114863, 127540, 171856, 270336, 383360, 392736, 459012, 623639, 960484, 1222656, 1312768, 1463990, 1480704, 2244736, 2380968, 3183563, 4161888, 4787280, 5107455, 5606400, 6826556, 7878400, 9188414, 9533238, 10219520, 10356472, 12981760, 15162808, 22062080, 25240360, 28313472, 32215040, 41284864, 72160576, 79563520, 91164167
Offset: 1

Views

Author

Robert G. Wilson v, Sep 02 2000

Keywords

Comments

No other terms below 10^8. - Max Alekseyev, Jul 10 2015

Crossrefs

Cf. A000009, A051177, A162468, A259943.

Programs

  • Mathematica
    Do[ If[ Mod[ PartitionsQ[n], n] == 0, Print[n]], {n, 1, 48000}]

Extensions

Extended by Max Alekseyev, Jul 04 2009
a(49)-a(60) from Max Alekseyev, Jul 10 2015

A128836 Numbers k such that partition number p(k) == 1 (mod k).

Original entry on oeis.org

1, 4, 7, 11, 54, 55, 115, 146, 157, 234, 239, 951, 272732, 419192, 7626972, 38355152
Offset: 1

Views

Author

Max Alekseyev, Klaus Brockhaus, Robert G. Wilson v and Zak Seidov, Mar 28 2007

Keywords

Comments

Numbers k such that A093952(k) = 1.
There are no other terms below 10^8. - Max Alekseyev, May 19 2014

Links

Crossrefs

Cf. A000041, A051177, A093952, A121015, A203023.

Extensions

a(16) from Max Alekseyev, Jan 15 2013

A121015 Numbers n such that partition number p(n) == 14 (mod n).

Original entry on oeis.org

1, 2, 8, 1402, 3579, 4111, 5289, 6383, 6467, 15146, 32141, 41910, 82849, 110088, 127531, 185114, 1320338, 1467242, 5739729, 22507473, 32494198
Offset: 1

Views

Author

Zak Seidov, Sep 02 2006

Keywords

Comments

No other terms below 10^8. - Max Alekseyev, May 19 2014

Examples

			Partition number of 8 is 22 = 1*8 + 14, hence 8 is a term.
Partition number of 1402 is 52435757789401123913939450130086135644 = 37400683159344596229628709079947315*1402 + 14, hence 1402 is a term.

Crossrefs

Cf. A000041, A051177, A093952, A128836, A203023.

Programs

  • Mathematica
    Do[ If[ Mod[ PartitionsP@n - 14, n] == 0, Print@n], {n, 731000}] (* Robert G. Wilson v, Sep 14 2006 *)
  • PARI
    for(n=1,200000,if((numbpart(n)-14)%n==0,print1(n,","))) \\ Klaus Brockhaus, Sep 07 2006

Extensions

Edited, corrected and extended (a(1) to a(3), a(11) to a(16)) by Klaus Brockhaus, Sep 07 2006
Rechecked by Klaus Brockhaus, Mar 17 2007
a(17)-a(19) from Ryan Propper, Mar 17 2007
a(20) from Max Alekseyev, Dec 28 2011
a(21) from Max Alekseyev, Jan 15 2013

A203023 Integers n dividing A000041(n)+1.

Original entry on oeis.org

1, 6, 156, 305, 484, 1219, 322733, 14343797, 58460571, 68355787
Offset: 1

Views

Author

Max Alekseyev, Dec 27 2011

Keywords

Comments

No other terms below 10^8.

Crossrefs

Cf. A093952, A051177, A128836, A121015

A299961 Numbers k such that k divides the number of overpartitions of k (A015128).

Original entry on oeis.org

1, 2, 12, 13, 22, 29, 88, 284, 370, 781, 1116, 1472, 1518, 1592, 2431, 2475, 2625, 3286, 5264, 6264, 6444, 7512, 7875, 9900, 22515, 30248, 30946, 31500, 32995, 41580, 69920, 112320, 126000, 140580, 142668, 166084, 166968, 225354, 232000, 272538, 290064, 312000
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 28 2018

Keywords

Examples

			284 is in the sequence because A015128(284) = 42480456349401075392 is divisible by 284.

Links

Crossrefs

Cf. A015128, A051177, A056848, A265835, A294086.

Extensions

More terms from Vaclav Kotesovec, Mar 02 2018

A304028 Numbers k such that A033461(k) is divisible by k.

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128, 2229, 2929, 3022, 4481, 34542, 34951, 36996, 58091, 292949, 437728, 438237, 2103581, 2237158, 3215950, 3375578
Offset: 1

Views

Author

Vaclav Kotesovec, May 04 2018

Keywords

Comments

A001422 is a finite subsequence.

Examples

			2229 is in the sequence because A033461(2229) = 51267 = 23 * 2229.

Crossrefs

Cf. A001422, A033461, A051177, A056848, A276517.

Programs

  • Mathematica
    max = 100; p = ConstantArray[0, max^2 + 1]; p[[1]] = 1; p[[2]] = 1; Do[Do[p[[j + 1]] += p[[j - k^2 + 1]], {j, max^2, k^2, -1}];, {k, 2, max}]; Select[Range[1, max^2], Divisible[p[[# + 1]], #] &]

A304040 Numbers k such that A026007(k) is divisible by k.

Original entry on oeis.org

1, 2, 4, 7, 11, 22, 61, 101, 217, 4846, 29419
Offset: 1

Views

Author

Vaclav Kotesovec, May 05 2018

Keywords

Comments

No other terms below 225000.

Examples

			217 is in the sequence because A026007(217) = 282948942888849443580867409 = 1303912179211287758437177 * 217.

Crossrefs

Cf. A026007, A051177, A056848, A285223, A304028.

A304043 Numbers k such that A022629(k) is divisible by k.

Original entry on oeis.org

1, 2, 5, 8, 28, 34, 50, 529, 1082, 1888, 42000, 112230, 178219
Offset: 1

Views

Author

Vaclav Kotesovec, May 05 2018

Keywords

Comments

No other terms below 1000000.

Examples

			50 is in the sequence because A022629(50) = 206309050 = 4126181 * 50.

Crossrefs

Cf. A022629, A051177, A056848, A304028, A304040.

A325630 Numbers k such that A000110(k) is divisible by k.

Original entry on oeis.org

1, 2, 35, 16833, 16989, 23684
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 07 2019

Keywords

Comments

No other terms below 50000.
From Amiram Eldar, Jun 20 2024: (Start)
Numbers k such that A166226(k) = 0.
All the terms above 2 are composites since A166226(p) == 2 (mod p) for prime p. (End)
No other terms below 90000. - Michael S. Branicky, Jan 09 2025

Examples

			35 is in the sequence because A000110(35) = 35 * 8045720086273150473238297902.

Crossrefs

Cf. A000110, A051130, A066562, A073877, A113883, A166226, A280727, A325935.
Cf. A014847, A016089, A023172, A051177, A056848.

Programs

  • Mathematica
    Select[Range[1000], Divisible[BellB[#], #] &]

A056872 Numbers k such that k | p(k) + q(k) where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).

Original entry on oeis.org

1, 5, 25, 42, 133, 618, 643, 701, 1962, 8150, 147458, 168459, 356038, 415870, 536685, 637757, 1093612, 1207618, 3368325, 3470706, 23400631, 37621653
Offset: 1

Views

Author

Robert G. Wilson v, Sep 02 2000

Keywords

Comments

No other terms below 10^8. - Max Alekseyev, Oct 12 2023

Crossrefs

Cf. A000009, A000041, A051177, A056848, A056873, A121919. A128836, A162468, A259943.

Programs

  • Mathematica
    Do[ If[ Mod[ PartitionsP[ n ] + PartitionsQ[ n ], n ] == 0, Print[ n ] ], {n, 1, 8150} ]

Extensions

a(11)-a(18) from Sean A. Irvine, May 12 2022
a(19)-a(22) from Max Alekseyev, Oct 12 2023
Showing 1-10 of 31 results. Next

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