OFFSET
0,4
COMMENTS
Definition: sigma(n,k)= sigma_k(n) = Sum_{d|n} d^k.
FORMULA
a(n) = Sum_{d|n} (d-1)^n for n>0 with a(0)=1.
MATHEMATICA
a[0] = 1; a[n_] := DivisorSum[n, (#-1)^n &]; Array[a, 20, 0] (* Amiram Eldar, Aug 15 2023 *)
PROG
(PARI) {a(n)=if(n==0, 1, sumdiv(n, d, (d-1)^n))}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n, (-1)^(n-k)*binomial(n, k)*sigma(n, k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 22 2009
STATUS
approved