This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A320416 #9 Oct 06 2020 03:23:50
%S A320416 1,1,8,31,110,380,1258,4145,13062,40549,123177,367524,1078214,3117641,
%T A320416 8889005,25019907,69592393,191419803,521053616,1404437257,3750615009,
%U A320416 9928671171,26065603448,67890853023,175503159857,450440887668,1148173347232,2907505610383,7316343339760,18299391020158,45503950232785,112518903733379
%N A320416 G.f.: exp( Sum_{n>=1} sigma_2(n)*sigma_3(n)/sigma(n) * x^n / n ), where sigma_{k}(n) equals the sum of the k-th powers of the divisors of n.
%C A320416 This sequence is conjectured to consist entirely of integers.
%C A320416 Related to A320917(n) = sigma_2(n)*sigma_3(n)/sigma(n).
%H A320416 Paul D. Hanna, <a href="/A320416/b320416.txt">Table of n, a(n) for n = 0..1000</a>
%e A320416 G.f.: A(x) = 1 + x + 8*x^2 + 31*x^3 + 110*x^4 + 380*x^5 + 1258*x^6 + 4145*x^7 + 13062*x^8 + 40549*x^9 + 123177*x^10 + ...
%e A320416 such that
%e A320416 log(A(x)) = x + 15*x^2/2 + 70*x^3/3 + 219*x^4/4 + 546*x^5/5 + 1050*x^6/6 + 2150*x^7/7 + 3315*x^8/8 + 5299*x^9/9 + 8190*x^10/10 + 13542*x^11/11 + 15330*x^12/12 + ... + sigma_2(n)*sigma_3(n)/sigma(n)*x^n/n + ...
%t A320416 nmax = 30; CoefficientList[Series[Exp[Sum[DivisorSigma[2, k]*DivisorSigma[3, k]/DivisorSigma[1, k] * x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 06 2020 *)
%o A320416 (PARI) {a(n) = polcoeff(exp( sum(m=1,n, sigma(m,2)*sigma(m,3)/sigma(m) *x^m/m ) +x*O(x^n)),n)}
%o A320416 for(n=0,35,print1(a(n),", "))
%Y A320416 Cf. A320917.
%K A320416 nonn
%O A320416 0,3
%A A320416 _Paul D. Hanna_, Oct 26 2018