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%I #22 Jun 03 2018 05:41:30
%S 1,1,0,1,2,1,1,3,3,2,3,4,5,6,6,8,9,8,12,15,14,17,21,20,24,31,30,34,42,
%T 41,46,59,63,67,76,83,94,104,112,131,144,144,170,198,201,226,261,268,
%U 291,337,361,392,437,465,511,567,607,673,736,775,861,946,1000
%N Expansion of Product_{k>=1} (1 + x^sigma(k)).
%H Vaclav Kotesovec, <a href="/A305321/b305321.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)
%p with(numtheory):
%p seq(coeff(series(mul(1+x^sigma(k),k=1..n), x,80),x,n),n=0..70); # _Muniru A Asiru_, May 31 2018
%t nmax = 100; CoefficientList[Series[Product[1 + x^DivisorSigma[1, k], {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 03 2018 *)
%o (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, 1+x^sigma(k)))
%Y Cf. A000203, A111865, A305320.
%K nonn
%O 0,5
%A _Seiichi Manyama_, May 30 2018