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A170925 G.f.: eta(q)*eta(q^2)*eta(q^4)*eta(q^8)*eta(q^16)*eta(q^32)*..., where eta(q) = Product((1-q^m), m=1..oo).

%I A170925 #19 Sep 23 2019 11:43:18
%S A170925 1,-1,-2,1,-1,3,3,-1,-2,-2,4,-4,-1,-3,-3,2,1,9,-1,6,7,-8,-10,1,-1,0,
%T A170925 -2,0,2,-1,4,-4,-1,-5,14,-15,-7,9,11,7,0,3,-14,17,-7,18,4,-6,-7,-25,
%U A170925 -12,-5,-13,-3,9,-14,25,10,-2,8,17,1,2,13,4,0,-4,7,13,-27,-42,11,5,5,10,-24,3,-21,-4,0,-32,27,29,-1,-4,43,26,-7,-41,-9,27,-11
%N A170925 G.f.: eta(q)*eta(q^2)*eta(q^4)*eta(q^8)*eta(q^16)*eta(q^32)*..., where eta(q) = Product((1-q^m), m=1..oo).
%C A170925 eta(q) = A(q)/A(q^2), where A(q) is the g.f. for this sequence (cf. A010815).
%H A170925 Seiichi Manyama, <a href="/A170925/b170925.txt">Table of n, a(n) for n = 0..10000</a>
%t A170925 nmax = 100; CoefficientList[Series[Product[QPochhammer[x^(2^k)], {k, 0, Log[nmax]/Log[2]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 23 2019 *)
%o A170925 (Ruby)
%o A170925 def s(k, n)
%o A170925   s = 0
%o A170925   (1..n).each{|i| s += i if n % i == 0 && i % k == 0}
%o A170925   s
%o A170925 end
%o A170925 def A(ary, n)
%o A170925   a_ary = [1]
%o A170925   a = [0] + (1..n).map{|i| ary.inject(0){|s, j| s + j[1] * s(j[0], i)}}
%o A170925   (1..n).each{|i| a_ary << (1..i).inject(0){|s, j| s - a[j] * a_ary[-j]} / i}
%o A170925   a_ary
%o A170925 end
%o A170925 def A170925(n)
%o A170925   A((0..Math.log(n, 2)).map{|i| [2 ** i, 1]}, n)
%o A170925 end
%o A170925 p A170925(100) # _Seiichi Manyama_, Sep 23 2019
%Y A170925 Cf. A010815, A083650, A030189, A160832, A143374, A194087.
%K A170925 sign
%O A170925 0,3
%A A170925 _N. J. A. Sloane_ and _Gary W. Adamson_, Feb 18 2010