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A162580 G.f.: A(x) = exp( 2*Sum_{n>=1} 2^[A007814(n)^2] * x^n/n ), where A007814(n) = exponent of highest power of 2 dividing n.

%I A162580 #9 Jul 04 2018 20:15:33
%S A162580 1,2,4,6,16,26,44,62,240,418,756,1094,2544,3994,6556,9118,32352,55586,
%T A162580 99492,143398,330000,516602,845900,1175198,3452112,5729026,9953556,
%U A162580 14178086,31076592,47975098,77547580,107120062,298608832,490097602
%N A162580 G.f.: A(x) = exp( 2*Sum_{n>=1} 2^[A007814(n)^2] * x^n/n ), where A007814(n) = exponent of highest power of 2 dividing n.
%H A162580 G. C. Greubel, <a href="/A162580/b162580.txt">Table of n, a(n) for n = 0..1000</a>
%e A162580 G.f.: A(x) = 1 + 2*x + 4*x^2 + 6*x^3 + 16*x^4 + 26*x^5 + 44*x^6 + ...
%e A162580 log(A(x))/2 = 2^0*x + 2^1*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^1*x^6/6 + 2^0*x^7/7 + 2^9*x^8/8 + ... + 2^[A007814(n)^2]*x^n/n + ...
%t A162580 nmax = 500; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(IntegerExponent[k, 2]^2 + 1)*q^k/k, {k, 1, nmax}]], {q,0,nmax}], n]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jul 04 2018 *)
%o A162580 (PARI) {a(n)=local(L=sum(m=1,n,2*2^(valuation(m,2)^2)*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}
%Y A162580 Cf. A155200, A007814, A000123, A162581, A162582.
%K A162580 nonn
%O A162580 0,2
%A A162580 _Paul D. Hanna_, Jul 06 2009