%I
%S 1,2,2,8,2,122,2,1682,10082,30242,2,7318082,2,17297282,3632428802,
%T 36843206402,2,2981705126402,2,1690185726028802,3379030566912002,
%U 28158588057602,2,76941821303636889602,1077167364120207360002
%N a(n) = Sum_{dn} n!/(d!*(n/d)!).
%C a(n) = 2 for prime n. It appears that all terms belong to A100195 (Numbers n such that the denominator of BernoulliB[n] is a record).  _Alexander Adamchuk_, Sep 09 2006
%C a(n) = 2 iff n is prime.
%C a(468) has 1007 decimal digits.  _Michael De Vlieger_, Sep 12 2018
%C From _Gus Wiseman_, Jan 10 2019: (Start)
%C 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:
%C [1 2 3 4]
%C .
%C [1 2] [1 2] [1 3] [1 3] [1 4] [1 4]
%C [3 4] [4 3] [2 4] [4 2] [2 3] [3 2]
%C .
%C [1]
%C [2]
%C [3]
%C [4]
%C (End)
%H Michael De Vlieger, <a href="/A121860/b121860.txt">Table of n, a(n) for n = 1..467</a>
%H Jimmy Devillet, Gergely Kiss, <a href="https://arxiv.org/abs/1806.02073">Characterizations of biselective operations</a>, arXiv:1806.02073 [math.RA], 2018.
%F E.g.f.: Sum_{k>0} (exp(x^k)1)/k!.
%t f[n_] := Block[{d = Divisors@n}, Plus @@ (n!/(d! (n/d)!))]; Array[f, 25] (* _Robert G. Wilson v_, Sep 11 2006 *)
%t Table[DivisorSum[n, n!/(#!*(n/#)!) &], {n, 25}] (* _Michael De Vlieger_, Sep 12 2018 *)
%o (PARI) a(n) = sumdiv(n, d, n!/(d!*(n/d)!)); \\ _Michel Marcus_, Sep 13 2018
%Y Cf. A038041, A057625, A061095, A100195, A236696, A320444.
%K easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Sep 09 2006
%E More terms from _Robert G. Wilson v_, Sep 11 2006
