A348397 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, 3, 3, 9, 3, 50, 3, 343, 734, 3388, 3, 133959, 3, 827646, 10297073, 33640713, 3, 2579172499, 3, 44822639761, 678610493345, 285312719194, 3, 393067887861756, 95367431640630, 302875123369476, 150094918113956098, 569940024192528003, 3, 105474401758856279784, 3

Offset: 1

Author

Wesley Ivan Hurt, Oct 16 2021

Keywords

• nonn

Examples

			a(6) = 50; a(6) = sigma_[6-1](1) + sigma_[6-2](2) + sigma_[6-3](3) + sigma_[6-6](6) = (1^5) + (1^4 + 2^4) + (1^3 + 3^3) + (6^0 + 6^0 + 6^0 + 6^0) = 50.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A321141.

Programs

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[n - #, #] &]; Array[a, 30] (* Amiram Eldar, Oct 17 2021 *)

PARI

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

Formula

a(n) = 3 iff n is prime. - Bernard Schott, Oct 17 2021