A356535 a(n) = Sum_{k=1..n} sigma_2(k)^2.

1, 26, 126, 567, 1243, 3743, 6243, 13468, 21749, 38649, 53533, 97633, 126533, 189033, 256633, 372914, 457014, 664039, 795083, 1093199, 1343199, 1715299, 1996199, 2718699, 3142500, 3865000, 4537400, 5639900, 6348864, 8038864, 8964308, 10827533, 12315933, 14418433

Offset: 1

Author

Vaclav Kotesovec, Aug 11 2022

Keywords

• nonn

Comments

Partial sums of A356533.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001157, A057434, A061502, A072379, A356536.

Cf. A127473, A035116, A072861, A356533, A356534.

Programs

Mathematica

Table[Sum[DivisorSigma[2, k]^2, {k, 1, n}], {n, 1, 40}]

PARI

a(n) = sum(k=1, n, sigma(k, 2)^2); \\ Michel Marcus, Aug 11 2022

Formula

a(n) ~ 189 * zeta(3)^2 * zeta(5) * n^5 / Pi^6.