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 1-5 of 5 results.

A078160 a(n) = A055086(n!).

Original entry on oeis.org

1, 2, 4, 8, 20, 52, 140, 400, 1203, 3808, 12634, 43771, 157821, 590518, 2287070, 9148286, 37719353, 160029667, 697553152, 3119552536, 14295585635, 67052240163, 321571247089, 1575370942644, 7876854713228, 40164235888490, 208699491618146, 1104333907134455, 5947020092025820
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Links

Crossrefs

Cf. A027423, A055086, A078155, A078159, A078161, A078162.

Programs

  • Mathematica
    Table[ Length[ Union[ Table[ Floor[w!/j], {j, 1, w!}]]], {w, 1, 11}]
a[n_] := Floor[Sqrt[4*n! + 1]] - 1; Array[a, 30] (* Amiram Eldar, Aug 18 2024 *)
  • PARI
    a(n)=sqrtint(4*n! + 1) - 1 \\ Charles R Greathouse IV, Mar 01 2018

Formula

a(n) = A027423(n) + A078155(n). - Amiram Eldar, Aug 18 2024

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
More terms from Charles R Greathouse IV, Mar 01 2018
a(25)-a(29) from Amiram Eldar, Aug 18 2024

A078156 A078153(n!).

Original entry on oeis.org

0, 0, 0, 0, 46, 702, 7479, 97902, 1231886, 15977798, 208298944, 3085485116, 45879947392, 749485746579, 12963973882204, 236404256556347, 4415737043058504, 88721524940832020, 1830113429944169943, 40228564066847381090, 921832573196324390682
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A078152, A078153, A078154, A078155, A078156, A078157, A078158.

Programs

  • Mathematica
    Table[Length[Union[Table[Floor[w!/j], {j, 1, w!}]]] -DivisorSigma[1, w! ], {w, 1, 9}]

Formula

a(n) = A078153(n!) = A078162(n) - A062569(n)

Extensions

Terms a(10) onward from Max Alekseyev, Feb 12 2012

A078161 a(n) = A051201(2^n).

Original entry on oeis.org

1, 3, 7, 15, 39, 87, 200, 438, 981, 2135, 4639, 9971, 21424, 45699, 97096, 205563, 433895, 913244, 1917491, 4016704, 8397235, 17521118, 36497171, 75900377, 157619705, 326868209, 676998896, 1400510860, 2894068715, 5974185368, 12320552102, 25385332979
Offset: 0

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A051201, A078159, A078160, A078162.

Programs

  • Mathematica
    Table[ Apply[ Plus, Union[ Table[ Floor[2^w/j], {j, 1, 2^w}]]], {w, 1, 25}]

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
Terms a(26) onward from Max Alekseyev, Feb 12 2012
a(0)=1 prepended by Alois P. Heinz, Oct 31 2023
a(21) corrected by Sean A. Irvine, Jun 18 2025

A078159 a(n) = A055086(2^n).

Original entry on oeis.org

2, 3, 4, 7, 10, 15, 21, 31, 44, 63, 89, 127, 180, 255, 361, 511, 723, 1023, 1447, 2047, 2895, 4095, 5791, 8191, 11584, 16383, 23169, 32767, 46339, 65535, 92680, 131071, 185362, 262143, 370726, 524287, 741454, 1048575, 1482909, 2097151, 2965819, 4194303, 5931640, 8388607
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Comments

a(2n-2)=2^n-1 and a(n)=2a(n-2)+1 generally.

Crossrefs

Cf. A055086, A078160, A078161, A078162.

Programs

  • Mathematica
    Table[ Length[ Union[ Table[ Floor[2^w/j], {j, 1, 2^w}]]], {w, 1, 25}]
  • PARI
    a(n) = ceil(2*sqrt(2^n+1)) - 2; \\ Michel Marcus, Sep 02 2019

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
More terms from Michel Marcus, Sep 02 2019

A078163 a(n) = A051201(n^2).

Original entry on oeis.org

1, 7, 19, 39, 66, 103, 146, 200, 263, 336, 418, 511, 611, 724, 848, 981, 1125, 1281, 1446, 1624, 1811, 2010, 2220, 2446, 2676, 2922, 3178, 3450, 3730, 4023, 4324, 4639, 4967, 5310, 5665, 6029, 6404, 6794, 7199, 7614, 8041, 8479, 8930, 9394, 9874
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A000290, A051201, A078161, A078162.

Programs

  • Mathematica
    Table[Apply[Plus, Union[Table[Floor[w^2/j], {j, 1, w^2}]]], {w, 1, 50}]
Showing 1-5 of 5 results.

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

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