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

Author

Leroy Quet, Jul 06 2005

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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 *)

PARI

a(n) = sum(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Dec 24 2017

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

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