A108639 a(n) = Sum_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = Sum_{j|k} j^m.

1, 3, 6, 13, 29, 77, 229, 771, 2863, 11573, 50365, 234161, 1156039, 6031751, 33130187, 190929778, 1151198268, 7243777234, 47462906927, 323188163753, 2282922216819, 16701529748621, 126359471558613, 987316752551419

Offset

1,2

Comments

Row sums of number triangle A109974. - Paul Barry, Jul 06 2005

Links

Michael De Vlieger, Table of n, a(n) for n = 1..599

Example

a(5) = 1^4 + (1^3 + 2^3) + (1^2 + 3^2) + (1^1 + 2^1 + 4^1) + (1^0 + 5^0) = 1 + 1 + 8 + 1 + 9 + 1 + 2 + 4 + 1 + 1 = 29.

Maple

with(numtheory): s:=proc(n, k) local div: div:=divisors(n): sum(div[j]^k, j=1..tau(n)) end: a:=n->sum(s(i, n-i), i=1..n): seq(a(n), n=1..27); # Emeric Deutsch, Jul 13 2005

Mathematica

Array[Sum[DivisorSigma[# - k, k], {k, #}] &, 24] (* Michael De Vlieger, Dec 23 2017 *)

Prog

(PARI) a(n) = sum(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Dec 24 2017
(Magma)
A108639:= func< n | (&+[DivisorSigma(j, n-j): j in [0..n-1]]) >;
[A108639(n): n in [1..30]]; // G. C. Greubel, Oct 18 2023
(SageMath)
def A108639(n): return sum(sigma(n-j, j) for j in range(n))
[A108639(n) for n in range(1, 31)] # G. C. Greubel, Oct 18 2023

Crossrefs

Cf. A109974, A245466 (with k instead of n-k).

Sequence in context: A093128 A005313 A213674 * A327795 A087218 A098075

Adjacent sequences: A108636 A108637 A108638 * A108640 A108641 A108642

Keyword

nonn

Author

Leroy Quet, Jul 06 2005

Extensions

More terms from Emeric Deutsch, Jul 13 2005

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007

Status

approved