|
| |
|
|
A308696
|
|
a(n) = Sum_{d|n} d^(2*d).
|
|
6
|
|
|
|
1, 17, 730, 65553, 9765626, 2176783082, 678223072850, 281474976776209, 150094635296999851, 100000000000009765642, 81402749386839761113322, 79496847203390846310290154, 91733330193268616658399616010, 123476695691247935826908004929122
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 1..214
|
|
|
FORMULA
|
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-1))) = Sum_{k>=1} a(k)*x^k/k.
G.f.: Sum_{k>=1} k^(2*k) * x^k/(1 - x^k).
|
|
|
MATHEMATICA
|
a[n_] := DivisorSum[n, #^(2*#) &]; Array[a, 14] (* Amiram Eldar, May 09 2021 *)
|
|
|
PROG
|
(PARI) {a(n) = sumdiv(n, d, d^(2*d))}
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-1)))))
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*k)*x^k/(1-x^k)))
|
|
|
CROSSREFS
|
Column k=2 of A308698.
Cf. A073705, A308753, A308756.
Sequence in context: A128274 A012085 A298306 * A308594 A308570 A218423
Adjacent sequences: A308693 A308694 A308695 * A308697 A308698 A308699
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Seiichi Manyama, Jun 17 2019
|
|
|
STATUS
|
approved
|
| |
|
|
