OFFSET
0,8
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
Convolution inverse of A107742.
a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A109386(k)*a(n-k) for n > 0.
G.f.: exp(-Sum_{k>=1} sigma(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Aug 26 2018
MAPLE
with(numtheory): seq(coeff(series(exp(-add(sigma(k)*x^k/(k*(1-x^(2*k))), k=1..n)), x, n+1), x, n), n = 0 .. 70); # Muniru A Asiru, Jan 30 2019
MATHEMATICA
A109386[n_] := DivisorSum[n, #*DivisorSum[#, Mod[#, 2] &] &]; a[0] = 1; a[n_] := a[n] = -(1/n) Sum[A109386[k] a[n-k], {k, 1, n}]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jun 04 2017 *)
CoefficientList[Series[1/Product[Product[1+x^(j*k), {j, 1, 100}], {k, 1, 100}], {x, 0, 80}], x] (* G. C. Greubel, Oct 29 2018 *)
PROG
(PARI) m=80; x='x+O('x^m); Vec(1/(prod(k=1, 2*m, prod(j=1, 2*m, 1+x^(j*k) )))) \\ G. C. Greubel, Oct 29 2018
(Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(&*[(&*[1 + x^(j*k): j in [1..2*m]]): k in [1..2*m]]))); // G. C. Greubel, Oct 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 04 2017
STATUS
approved