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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A320917. Sequence in context: A212064 A213764 A335606 * A289613 A055845 A034556 Adjacent sequences: A320413 A320414 A320415 * A320417 A320418 A320419 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 26 2018 STATUS approved

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Last modified September 21 19:32 EDT 2023. Contains 365503 sequences. (Running on oeis4.)