A279964 a(n) = Sum_{k=1..n-1} sigma_3(k)*sigma_7(n-k).

0, 1, 138, 3377, 39890, 297550, 1623980, 7065329, 25808790, 82305816, 234756742, 611706830, 1474831246, 3334313204, 7118797268, 14485772017, 28206850488, 52921773667, 95877425634, 168644231672, 288301373792, 481166453010, 784226941604, 1253068878542, 1962356045590

Offset: 1

Author

Seiichi Manyama, Dec 23 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000594, A001158, A001160, A013955, A279889.

Programs

Mathematica

Table[Sum[DivisorSigma[3, k] * DivisorSigma[7, n - k], {k, 1, n - 1}], {n, 1, 25}] (* Indranil Ghosh, Mar 12 2017 *)
a[n_] := (1800 * RamanujanTau[n] + 273 * DivisorSigma[11, n] - 1382 * DivisorSigma[7, n] - 691 * DivisorSigma[3, n]) / 331680; Array[a, 25] (* Amiram Eldar, Jan 07 2025 *)

PARI

a(n) = sum(k=1, n-1, sigma(k, 3)*sigma(n-k,7)); \\ Michel Marcus, Dec 24 2016

PARI

a(n) = {my(f = factor(n)); (1800 * ramanujantau(n) + 273 * sigma(f, 11) - 1382 * sigma(f, 7) - 691 * sigma(f, 3)) / 331680;} \\ Amiram Eldar, Jan 07 2025

Formula

36*tau(n) = 5*sigma_3(n) + 10*sigma_7(n) + 21*sigma_5(n) + 2400*a(n) - 5292*A279889(n).