OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..305
FORMULA
E.g.f.: Sum_{k>0} (exp((k * x)^k) - 1)/(k^k * k!).
If p is prime, a(p) = 2.
MAPLE
f:= proc(n) local d; n! * add(d^(n-d)/(d! * (n/d)!), d = numtheory:-divisors(n)) end proc:
map(f, [$1..30]); # Robert Israel, Jul 10 2023
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^(n - #)/(#! * (n/#)!) &]; Array[a, 23] (* Amiram Eldar, Jun 11 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, d^(n-d)/(d!*(n/d)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/(k^k*k!))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 11 2022
STATUS
approved