OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..449
FORMULA
E.g.f.: Sum_{k>0} log(1+x^k)/k!.
E.g.f.: -Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k. - Seiichi Manyama, Jun 18 2023
MAPLE
restart;
f:= proc(n) local d;
add((-1)^(n/d + 1) * (n-1)!/(d-1)!, d = numtheory:-divisors(n))
end proc:
map(f, [$1..30]); # Robert Israel, Nov 14 2024
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(n/#+1) * (n-1)!/(#-1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 28 2022
STATUS
approved