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 1-3 of 3 results.

A141323 Number of groups of order L(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 5, 1, 1, 4, 1, 1, 4, 2, 1, 9, 1, 1, 30, 1, 1, 11, 5, 1, 4, 1, 2, 9, 2, 1
Offset: 0

Views

Author

Jonathan Vos Post, Aug 02 2008

Keywords

Comments

This is to A140987 as Lucas numbers A000032 are to Fibonacci numbers A000045.

Examples

			a(6) = 5 because the Lucas number L(6) (starting at L(0) = 2) is 18 and there are 5 groups of order 18.

Links

Crossrefs

Cf. A000001, A000032, A000045, A140987.

Formula

a(n) = A000001(A000032(n)).

Extensions

a(16)-a(29) from Eric M. Schmidt, Jun 20 2014

A282460 Number of groups of order n^2.

Original entry on oeis.org

0, 1, 2, 2, 14, 2, 14, 2, 267, 15, 16, 2, 197, 2, 12, 6, 56092, 2, 176, 2, 221, 13, 12, 2, 8681, 15, 16, 504, 172, 2, 150, 2, 49487367289, 6, 16, 4, 3609, 2, 12, 13, 10281, 2, 228, 2, 167, 63, 12, 2, 15756130, 15, 227, 7, 219, 2, 7199, 15, 8085, 21, 16, 2, 4484
Offset: 0

Views

Author

Vincenzo Librandi, Feb 16 2017

Keywords

Links

Crossrefs

Cf. A000001, A000679, A140987, A141323, A235388.

Programs

  • Magma
    D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n^2) : n in [1..31] ];
  • Mathematica
    Join[{0}, FiniteGroupCount[Range[45]^2]]

Formula

a(n) = A000001(n^2). - R. J. Mathar, Feb 23 2017

Extensions

a(32) corrected by David Burrell, Jun 07 2022
Terms a(46) and beyond from Max Horn's website added by Andrey Zabolotskiy, May 14 2023

A297420 Square of the number of groups of order n.

Original entry on oeis.org

0, 1, 1, 1, 4, 1, 4, 1, 25, 4, 4, 1, 25, 1, 4, 1, 196, 1, 25, 1, 25, 4, 4, 1, 225, 4, 4, 25, 16, 1, 16, 1, 2601, 1, 4, 1, 196, 1, 4, 4, 196, 1, 36, 1, 16, 4, 4, 1, 2704, 4, 25, 1, 25, 1, 225, 4, 169, 4, 4, 1, 169, 1, 4, 16, 71289, 1, 16, 1, 25, 1, 16, 1, 2500
Offset: 0

Views

Author

Vincenzo Librandi, Dec 31 2017

Keywords

Comments

The record values are 1, 4, 25, 196, 225, 2601, 2704, 71289, 5419584, 3146312464, 110128506489369, 2448999521196387209521, etc. (A046058)

Links

Crossrefs

Cf. A000001, A000679, A140987, A141323, A235388, A282460.

Programs

  • GAP
    Concatenation([0], List([1..100], n -> NumberSmallGroups(n)^2)); # Muniru A Asiru, Jan 29 2018
  • Magma
    D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n)^2 : n in [1..100] ];
  • Maple
    with(GroupTheory):  0,seq(NumGroups(n)^2, n=1..100); # Muniru A Asiru, Jan 29 2018
  • Mathematica
    Join[{0}, FiniteGroupCount[Range[200]]^2]

Formula

a(n) = A000001(n)^2.

Extensions

Name clarified by Jon E. Schoenfield, May 24 2019
Showing 1-3 of 3 results.

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

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