cp's OEIS Frontend

A198301 G.f.: exp( Sum_{n>=1} (x^n/n) * Sum_{d|n} d*sigma(n/d,d) ).

%I A198301 #9 Mar 30 2012 18:37:31
%S A198301 1,1,3,5,12,18,42,62,131,206,398,610,1203,1810,3358,5260,9471,14518,
%T A198301 26182,39906,70320,108849,187251,287525,497288,758860,1286936,1986352,
%U A198301 3330677,5102712,8560107,13070327,21685731,33328561,54744685,83792111,137817745,210223967
%N A198301 G.f.: exp( Sum_{n>=1} (x^n/n) * Sum_{d|n} d*sigma(n/d,d) ).
%C A198301 Here sigma(n,k) is the sum of the k-th powers of the divisors of n.
%F A198301 G.f.: exp( Sum_{n>=1} Sum_{k>=1} sigma(n,k) * x^(n*k)/n ).
%F A198301 Logarithmic derivative yields A198302.
%e A198301 G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 12*x^4 + 18*x^5 + 42*x^6 + 62*x^7 +...
%e A198301 where the logarithm begins:
%e A198301 log(A(x)) = x + 5*x^2/2 + 7*x^3/3 + 21*x^4/4 + 11*x^5/5 + 65*x^6/6 + 15*x^7/7 + 133*x^8/8 + 106*x^9/9 +...+ A198302(n)*x^n/n +...
%o A198301 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,sumdiv(m, d, d*sigma(m/d,d))*x^m/m)+x*O(x^n)),n)}
%o A198301 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,sum(k=1,n\m,sigma(m,k)*x^(m*k)/m)+x*O(x^n))),n)}
%Y A198301 Cf. A198302 (log), A198296.
%K A198301 nonn
%O A198301 0,3
%A A198301 _Paul D. Hanna_, Jan 27 2012