cp's OEIS Frontend

A224439 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^(n-1) * x^n/n ).

%I A224439 #15 Nov 11 2017 04:45:11
%S A224439 1,1,2,7,93,357,41927,80065,21483964,112388242,19973468103,
%T A224439 25813956365,691174602929572,695655501206181,63995738768530056,
%U A224439 1469847380380956056,1468171845473348201557,1477216529008886240457,62064992121198579569054696,62086294811417506896412871
%N A224439 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^(n-1) * x^n/n ).
%C A224439 Compare to g.f. of partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.
%H A224439 Seiichi Manyama, <a href="/A224439/b224439.txt">Table of n, a(n) for n = 0..335</a>
%F A224439 a(n) = (1/n)*Sum_{k=1..n} sigma(k)^(k-1) * a(n-k) for n > 0, with a(0)=1.
%F A224439 Logarithmic derivative yields A224440.
%e A224439 G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 93*x^4 + 357*x^5 + 41927*x^6 + ... where
%e A224439 log(A(x)) = x + 3^1*x^2/2 + 4^2*x^3/3 + 7^3*x^4/4 + 6^4*x^5/5 + 12^5*x^6/6 + ...
%o A224439 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m)^(m-1)*x^m/m)+x*O(x^n)), n)}
%o A224439 for(n=0, 20, print1(a(n), ", "))
%o A224439 (PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sigma(k)^(k-1)*a(n-k)))}
%Y A224439 Cf. A224440, A156217, A158095, A000203.
%K A224439 nonn
%O A224439 0,3
%A A224439 _Paul D. Hanna_, Apr 06 2013