OFFSET
0,3
COMMENTS
This sequence is conjectured to consist entirely of integers.
Related to A320917(n) = sigma_2(n)*sigma_3(n)/sigma(n).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1000
EXAMPLE
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 + ...
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 *)
PROG
(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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 26 2018
STATUS
approved