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A308693 a(n) = Sum_{d|n} d^(3*(n/d - 1)). 2
1, 2, 2, 10, 2, 93, 2, 578, 731, 4223, 2, 56765, 2, 262489, 547068, 2359810, 2, 31173510, 2, 152949071, 387538140, 1073743157, 2, 20134371189, 244140627, 68719478935, 282430067924, 618515646977, 2, 12056339359929, 2, 39582552821762, 205891133866212 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..33.

FORMULA

L.g.f.: -log(Product_{k>=1} (1 - k^3*x^k)^(1/k^4)) = Sum_{k>=1} a(k)*x^k/k.

a(p) = 2 for prime p.

G.f.: Sum_{k>=1} x^k/(1 - k^3*x^k). - Ilya Gutkovskiy, Jul 25 2019

PROG

(PARI) {a(n) = sumdiv(n, d, d^(3*(n/d-1)))}

(PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^3*x^k)^(1/k^4)))))

CROSSREFS

Column k=3 of A308694.

Sequence in context: A137450 A321415 A319692 * A163937 A083457 A163808

Adjacent sequences:  A308690 A308691 A308692 * A308694 A308695 A308696

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 17 2019

STATUS

approved

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Last modified March 6 03:35 EST 2021. Contains 341841 sequences. (Running on oeis4.)