|
|
A308757
|
|
a(n) = Sum_{d|n} d^(3*(d-2)).
|
|
2
|
|
|
1, 2, 28, 4098, 1953126, 2176782365, 4747561509944, 18014398509486082, 109418989131512359237, 1000000000000000001953127, 13109994191499930367061460372, 237376313799769806328952468217885, 5756130429098929077956071497934208654
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(3*k-7))) = Sum_{k>=1} a(k)*x^k/k.
G.f.: Sum_{k>=1} k^(3*(k-2)) * x^k/(1 - x^k).
|
|
MATHEMATICA
|
a[n_] := DivisorSum[n, #^(3*(# - 2)) &]; Array[a, 13] (* Amiram Eldar, May 08 2021 *)
|
|
PROG
|
(PARI) {a(n) = sumdiv(n, d, d^(3*(d-2)))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k-7)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(3*(k-2))*x^k/(1-x^k)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|