A386877 -id:A386877 - cp's OEIS frontend

1, 2, 2, 8, 2, 122, 2, 1682, 10082, 30242, 2, 7318082, 2, 17297282, 3632428802, 36843206402, 2, 2981705126402, 2, 1690185726028802, 3379030566912002, 28158588057602, 2, 76941821303636889602, 1077167364120207360002

Offset: 1

Vladeta Jovovic, Sep 09 2006

a(n) = 2 iff n is prime.
a(468) has 1007 decimal digits. - Michael De Vlieger, Sep 12 2018
From Gus Wiseman, Jan 10 2019: (Start)
Number of matrices whose entries are 1,...,n, up to row and column permutations. For example, inequivalent representatives of the a(4) = 8 matrices are:
  [1 2 3 4]
.
  [1 2] [1 2] [1 3] [1 3] [1 4] [1 4]
  [3 4] [4 3] [2 4] [4 2] [2 3] [3 2]
.
  [1]
  [2]
  [3]
  [4]
(End)
Conjecture: the sequence a(n) taken modulo a positive integer k >= 3 eventually becomes constant equal to 2. For example, the sequence taken modulo 11 is [1, 2, 2, 8, 2, 1, 2, 10, 6, 3, 2, 2, 2, 2, 2, 2, ...]. - Peter Bala, Aug 08 2025

Michael De Vlieger, Table of n, a(n) for n = 1..467
Jimmy Devillet, Gergely Kiss, Characterizations of biselective operations, arXiv:1806.02073 [math.RA], 2018.

Cf. A038041, A057625, A061095, A100195, A236696, A258899, A258903, A320444, A386877.

with(numtheory): seq(n!*add(1/(d!*(n/d)!), d in divisors(n)), n = 1..25); # Peter Bala, Aug 04 2025

f[n_] := Block[{d = Divisors@n}, Plus @@ (n!/(d! (n/d)!))]; Array[f, 25] (* Robert G. Wilson v, Sep 11 2006 *)
Table[DivisorSum[n, n!/(#!*(n/#)!) &], {n, 25}] (* Michael De Vlieger, Sep 12 2018 *)

a(n) = sumdiv(n, d, n!/(d!*(n/d)!)); \\ Michel Marcus, Sep 13 2018

E.g.f.: Sum_{k>0} (exp(x^k)-1)/k!.

More terms from Robert G. Wilson v, Sep 11 2006

cp's OEIS Frontend

A121860 a(n) = Sum_{d|n} n!/(d!*(n/d)!).

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