A376290 a(n) = Sum_{k=1..n-1} sigma_2(k) * sigma_3(n-k).

0, 1, 14, 83, 324, 986, 2484, 5625, 11304, 21596, 37824, 64746, 103252, 163536, 244200, 364855, 517478, 741087, 1009244, 1394080, 1842690, 2470668, 3178188, 4171260, 5242610, 6735966, 8331338, 10511692, 12777898, 15922212, 19067506, 23429969, 27785000, 33707290

Offset: 1

Author

Vaclav Kotesovec, Sep 19 2024

Keywords

• nonn

Comments

In general, if k>=1, m>=1 and a(n) = Sum_{j=1..n-1} sigma_k(j) * sigma_m(n-j), then Sum_{j=1..n} a(j) ~ Gamma(k+1) * Gamma(m+1) * zeta(k+1) * zeta(m+1) * n^(k+m+2) / Gamma(k+m+3).

Crossrefs

Cf. A001157, A001158, A374974, A374963.

Programs

Mathematica

Table[Sum[DivisorSigma[2, k]*DivisorSigma[3, n-k], {k, n-1}], {n, 1, 50}]

PARI

a(n) = sum(k=1, n-1, sigma(k, 2) * sigma(n-k, 3)); \\ Michel Marcus, Sep 19 2024

Formula

Sum_{k=1..n} a(k) ~ Pi^4 * zeta(3) * n^7 / 37800.