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A344043
a(n) = n * Sum_{d|n} sigma(d)^3 / d.
4
1, 29, 67, 401, 221, 1943, 519, 4177, 2398, 6409, 1739, 26867, 2757, 15051, 14807, 38145, 5849, 69542, 8019, 88621, 34773, 50431, 13847, 279859, 30896, 79953, 71194, 208119, 27029, 429403, 32799, 326337, 116513, 169621, 114699, 961598, 54909, 232551, 184719, 923117, 74129, 1008417, 85227, 697339
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k >= 1} sigma(k)^3 * x^k/(1 - x^k)^2.
Sum_{k=1..n} a(k) ~ c * n^4, where c = (Pi^6*zeta(3)^2/2160) * Product_{p prime} (1 + 2/p^2 + 2/p^3 + 1/p^5) = 1.8238925519... . - Amiram Eldar, Nov 20 2022
MATHEMATICA
a[n_] := n * DivisorSum[n, DivisorSigma[1, #]^3/# &]; Array[a, 44] (* Amiram Eldar, May 08 2021 *)
PROG
(PARI) a(n) = n*sumdiv(n, d, sigma(d)^3/d);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^3*x^k/(1-x^k)^2))
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 08 2021
STATUS
approved