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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
1, 8, 32, 301, 3132, 47764, 823552, 16847478, 387440943, 10009869956, 285311670624, 8918297605544, 302875106592268, 11112685154884700, 437893920913552704, 18447025557293175687, 827240261886336764196, 39346558271690970332766, 1978419655660313589124000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 17:21 EST 2023. Contains 360128 sequences. (Running on oeis4.)