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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

%I

%S 1,8,32,301,3132,47764,823552,16847478,387440943,10009869956,

%T 285311670624,8918297605544,302875106592268,11112685154884700,

%U 437893920913552704,18447025557293175687,827240261886336764196,39346558271690970332766,1978419655660313589124000

%N 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.

%F 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

%e 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.

%t a[n_] := DivisorSum[n, DivisorSigma[#, n] &]; Array[a, 20] (* _Amiram Eldar_, Oct 17 2021 *)

%o (PARI) a(n) = sumdiv(n, d, sigma(n, d)); \\ _Michel Marcus_, Oct 18 2021

%Y Cf. A321141.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Oct 16 2021

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)