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A205479 L.g.f.: Sum_{n>=1} (x^n/n) * Product_{d|n} (1 + d*x^n).

%I A205479 #13 May 23 2021 06:25:20
%S A205479 1,3,1,7,1,15,1,15,10,13,1,67,1,17,16,63,1,168,1,37,22,25,1,555,1,29,
%T A205479 118,49,1,520,1,543,34,37,1,1048,1,41,40,1125,1,554,1,73,475,49,1,
%U A205479 6651,1,563,52,85,1,1680,1,1457,58,61,1,20632,1,65,787,5087,1
%N A205479 L.g.f.: Sum_{n>=1} (x^n/n) * Product_{d|n} (1 + d*x^n).
%H A205479 Antti Karttunen, <a href="/A205479/b205479.txt">Table of n, a(n) for n = 1..2201</a>
%F A205479 Forms the logarithmic derivative of A205478.
%e A205479 L.g.f.: L(x) = x + 3*x^2/2 + x^3/3 + 7*x^4/4 + x^5/5 + 15*x^6/6 +...
%e A205479 By definition:
%e A205479 L(x) = x*(1+x) + x^2*(1+x^2)*(1+2*x^2)/2 + x^3*(1+x^3)*(1+3*x^3)/3 + x^4*(1+x^4)*(1+2*x^4)*(1+4*x^4)/4 + x^5*(1+x^5)*(1+5*x^5)/5 + x^6*(1+x^6)*(1+2*x^6)*(1+3*x^6)*(1+6*x^6)/6 +...
%e A205479 Exponentiation yields the g.f. of A205478:
%e A205479 exp(L(x)) = 1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 8*x^6 + 8*x^7 +...
%t A205479 max = 70; s = Sum[(x^(n-1)/n)*Product[1+d*x^n, {d, Divisors[n]}], {n, 1, max}] + O[x]^max; CoefficientList[s, x]*Range[max] (* _Jean-François Alcover_, Dec 23 2015 *)
%o A205479 (PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, log(1+d*x^m+x*O(x^n))))), n)}
%Y A205479 Cf. A205478 (exp), A205477, A205481, A205483, A205485, A205487, A205489, A205491.
%K A205479 nonn
%O A205479 1,2
%A A205479 _Paul D. Hanna_, Jan 27 2012