A348399 a(n) = Sum_{d|n} sigma_[d](n), where sigma_[k](n) is the sum of the k-th powers of the divisors of n.

1, 8, 32, 301, 3132, 47764, 823552, 16847478, 387440943, 10009869956, 285311670624, 8918297605544, 302875106592268, 11112685154884700, 437893920913552704, 18447025557293175687, 827240261886336764196, 39346558271690970332766, 1978419655660313589124000

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

a(p) = p^p + p + 2 for primes p, since we have a(p) = sigma_[1](p) + sigma[p](p) = (1 + p) + (1^p + p^p) = p^p + p + 2. - Wesley Ivan Hurt, Nov 03 2021

Example

a(4) = 301; a(4) = sigma_[1](4) + sigma_[2](4) + sigma_[4](4) = (1^1 + 2^1 + 4^1) + (1^2 + 2^2 + 4^2) + (1^4 + 2^4 + 4^4) = 301.

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[#, n] &]; Array[a, 20] (* Amiram Eldar, Oct 17 2021 *)

Prog

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

Crossrefs

Cf. A321141.

Sequence in context: A093759 A066415 A143557 * A208824 A034193 A159277

Adjacent sequences: A348396 A348397 A348398 * A348400 A348401 A348402

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 16 2021

Status

approved