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 A321598 a(n) = Sum_{d|n} d*binomial(d+2,3). 0
 1, 9, 31, 89, 176, 375, 589, 1049, 1516, 2384, 3147, 4823, 5916, 8437, 10406, 14105, 16474, 22380, 25271, 33264, 37810, 47683, 52901, 68183, 73301, 91100, 100174, 122197, 130356, 161750, 169137, 205593, 219162, 259242, 272714, 330524, 338144, 400719, 421686, 493424 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Inverse MÃ¶bius transform of A002417. LINKS N. J. A. Sloane, Transforms FORMULA G.f.: Sum_{k>=1} x^k*(1 + 3*x^k)/(1 - x^k)^5. G.f.: Sum_{k>=1} k*A000292(k)*x^k/(1 - x^k). L.g.f.: -log(Product_{k>=1} (1 - x^k)^A000292(k)) = Sum_{n>=1} a(n)*x^n/n. Dirichlet g.f.: (zeta(s-4) + 3*zeta(s-3) + 2*zeta(s-2))*zeta(s)/6. a(n) = (2*sigma_2(n) + 3*sigma_3(n) + sigma_4(n))/6. a(n) = Sum_{d|n} A002417(d). Sum_{k=1..n} a(k) ~ Zeta(5) * n^5 / 30. - Vaclav Kotesovec, Feb 02 2019 MATHEMATICA Table[Sum[d Binomial[d + 2, 3], {d, Divisors[n]}], {n, 40}] nmax = 40; Rest[CoefficientList[Series[Sum[x^k (1 + 3 x^k)/(1 - x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x]] Table[(2 DivisorSigma[2, n] + 3 DivisorSigma[3, n] + DivisorSigma[4, n])/6, {n, 40}] CROSSREFS Cf. A000292, A000335, A001157, A001158, A001159, A002417, A059358, A278403. Sequence in context: A177342 A224000 A118444 * A048374 A226274 A184054 Adjacent sequences:  A321595 A321596 A321597 * A321599 A321600 A321601 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 14 2018 STATUS approved

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Last modified September 26 18:49 EDT 2020. Contains 337374 sequences. (Running on oeis4.)