cp's OEIS Frontend

A205483 L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d.

%I A205483 #8 Aug 22 2025 17:57:56
%S A205483 1,3,1,11,1,45,1,59,109,53,1,869,1,101,961,3643,1,3555,1,18101,3235,
%T A205483 245,1,92645,21876,341,11287,74141,1,722045,1,324667,20329,581,502076,
%U A205483 5280611,1,725,40054,7567509,1,27239663,1,906301,7838224,1061,1,181474021
%N A205483 L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d.
%F A205483 Forms the logarithmic derivative of A205482.
%e A205483 L.g.f.: L(x) = x + 3*x^2/2 + x^3/3 + 11*x^4/4 + x^5/5 + 45*x^6/6 +...
%e A205483 By definition:
%e A205483 L(x) = x*(1+x) + x^2*(1+x^2)*(1+2*x^2)^2/2 + x^3*(1+x^3)*(1+3*x^3)^3/3 + x^4*(1+x^4)*(1+2*x^4)^2*(1+4*x^4)^4/4 + x^5*(1+x^5)*(1+5*x^5)^5/5 + x^6*(1+x^6)*(1+2*x^6)^2*(1+3*x^6)^3*(1+6*x^6)^6/6 +...
%e A205483 Exponentiation yields the g.f. of A205482:
%e A205483 exp(L(x)) = 1 + x + 2*x^2 + 2*x^3 + 5*x^4 + 5*x^5 + 15*x^6 + 15*x^7 +...
%o A205483 (PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, d*log(1+d*x^m+x*O(x^n))))), n)}
%Y A205483 Cf. A205482 (exp), A205477, A205479, A205481, A205485, A205487, A205489, A205491.
%K A205483 nonn
%O A205483 1,2
%A A205483 _Paul D. Hanna_, Jan 27 2012