A343781 a(n) = Sum_{k=1..floor(n/2)} sigma_k(n-k), where sigma_k(n) is the sum of the k-th powers of the divisors of n.

0, 1, 3, 9, 17, 55, 111, 457, 943, 4962, 11148, 69526, 159402, 1161340, 2765874, 22829766, 55192956, 510771772, 1257880780, 12870681814, 32042113008, 359566186586, 904795505226, 11043196798176, 28002785395660, 369463867367567, 943392140873807, 13378621275148931

Offset: 1

Author

Wesley Ivan Hurt, Apr 29 2021

Keywords

• nonn

Examples

			a(5) = 17; a(5) = Sum_{i=1..2} sigma_k(5-k) = sigma_1(4) + sigma_2(3) = (1+2+4) + (1^2+3^2) = 7 + 10 = 17.
		

Crossrefs

Cf. A245466.

Programs

Mathematica

Table[Sum[DivisorSigma[i, n - i], {i, Floor[n/2]}], {n, 30}]

PARI

a(n) = sum(k=1, n\2, sigma(n-k, k)); \\ Michel Marcus, Apr 29 2021