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A308692 a(n) = Sum_{d|n} d^(2*(n/d - 1)). 5
1, 2, 2, 6, 2, 27, 2, 82, 83, 283, 2, 2047, 2, 4147, 7188, 20546, 2, 125964, 2, 343407, 533844, 1048699, 2, 10076747, 390627, 16777387, 43053284, 84003927, 2, 667311413, 2, 1342439682, 3486799044, 4294967587, 249905428, 52916914768, 2, 68719477099, 282429565044 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..3143

FORMULA

L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.

a(p) = 2 for prime p.

G.f.: Sum_{k>=1} x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019

MAPLE

N:=100: # for a(1)..a(N)

g:= add(x^k/(1-k^2*x^k), k=1..N):

S:= series(g, x, N+1):

seq(coeff(S, x, j), j=1..N); # Robert Israel, Apr 05 2020

PROG

(PARI) {a(n) = sumdiv(n, d, d^(2*(n/d-1)))}

(PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^2*x^k)^(1/k^3)))))

CROSSREFS

Column k=2 of A308694.

Sequence in context: A286376 A100346 A306387 * A319352 A300834 A293214

Adjacent sequences:  A308689 A308690 A308691 * A308693 A308694 A308695

KEYWORD

nonn,look

AUTHOR

Seiichi Manyama, Jun 17 2019

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)