A348398 a(n) = Sum_{d|n} sigma_[n/d](d), where sigma_[k](n) is the sum of the k-th powers of the divisors of n.

1, 4, 5, 13, 7, 32, 9, 54, 42, 78, 13, 299, 15, 204, 395, 647, 19, 1626, 21, 2881, 2565, 2208, 25, 17070, 3158, 8406, 20482, 35607, 31, 116964, 33, 136104, 178529, 131418, 94983, 1112928, 39, 524712, 1596579, 2533908, 43, 7283718, 45, 8405995, 16364934, 8389212, 49, 78586033, 823602, 43423962

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

a(8) = 54; a(8) = sigma_[8/1](1) + sigma_[8/2](2) + sigma_[8/4](4) + sigma_[8/8](8) = (1^8) + (1^4 + 2^4) + (1^2 + 2^2 + 4^2) + (1^1 + 2^1 + 4^1 + 8^1) = 54.

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[n/#, #] &]; Array[a, 50] (* Amiram Eldar, Oct 17 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, sigma(d, n/d)); \\ Michel Marcus, Oct 18 2021

Crossrefs

Cf. A321141.

Sequence in context: A028272 A003969 A326828 * A132140 A102703 A283483

Adjacent sequences: A348395 A348396 A348397 * A348399 A348400 A348401

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 16 2021

Status

approved