login
A308755
a(n) = Sum_{d|n} d^(d-2).
3
1, 2, 4, 18, 126, 1301, 16808, 262162, 4782973, 100000127, 2357947692, 61917365541, 1792160394038, 56693912392105, 1946195068359504, 72057594038190098, 2862423051509815794, 121439531096599036046, 5480386857784802185940, 262144000000000100000143
OFFSET
1,2
LINKS
FORMULA
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k-3))) = Sum_{k>=1} a(k)*x^k/k.
G.f.: Sum_{k>=1} k^(k-2) * x^k/(1 - x^k).
MATHEMATICA
a[n_] := DivisorSum[n, #^(# - 2) &]; Array[a, 20] (* Amiram Eldar, May 08 2021 *)
PROG
(PARI) {a(n) = sumdiv(n, d, d^(d-2))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(k-3)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(k-2)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 22 2019
STATUS
approved