A356536 -id:A356536 - cp's OEIS frontend

A356534 a(n) = sigma_3(n)^2.

1, 81, 784, 5329, 15876, 63504, 118336, 342225, 573049, 1285956, 1774224, 4177936, 4831204, 9585216, 12446784, 21911761, 24147396, 46416969, 47059600, 84603204, 92775424, 143712144, 148060224, 268304400, 248094001, 391327524, 417793600, 630612544, 594872100

Offset: 1

Vaclav Kotesovec, Aug 11 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000
Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (15), a=b=3.

Cf. A001158, A127473, A035116, A072861, A356536 (partial sums).

Mathematica
```
Table[DivisorSigma[3, n]^2, {n, 1, 40}]
```

a(n) = sigma(n, 3)^2; \\ Michel Marcus, Aug 11 2022

Dirichlet g.f.: zeta(s) * zeta(s-3)^2 * zeta(s-6) / zeta(2*s-6).

Multiplicative with a(p^e) = ((p^(3*e+3)-1)/(p^3-1))^2. - Amiram Eldar, Aug 11 2022

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

Original entry on oeis.org

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

Vaclav Kotesovec, Aug 11 2022

nonn

Partial sums of A356533.

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

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

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

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

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

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

cp's OEIS Frontend

A356534 a(n) = sigma_3(n)^2.

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