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.
1, 1, 8, 31, 110, 380, 1258, 4145, 13062, 40549, 123177, 367524, 1078214, 3117641, 8889005, 25019907, 69592393, 191419803, 521053616, 1404437257, 3750615009, 9928671171, 26065603448, 67890853023, 175503159857, 450440887668, 1148173347232, 2907505610383, 7316343339760, 18299391020158, 45503950232785, 112518903733379
Offset: 0
Keywords
Examples
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 + ... such that 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 + ...
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..1000
Crossrefs
Cf. A320917.
Programs
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Mathematica
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 *) -
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)} for(n=0,35,print1(a(n),", "))
Comments