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

1,2

Links

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

Formula

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

Example

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.

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[n - #, #] &]; Array[a, 30] (* 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: A157031 A113213 A088032 * A377398 A066572 A307379

Adjacent sequences: A348394 A348395 A348396 * A348398 A348399 A348400

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 16 2021

Status

approved