A350801 a(n) = n*(tau(n) + 1) - 2*sigma(n) for n>=1, with a(0)=0.

0, 0, 0, 1, 2, 3, 6, 5, 10, 10, 14, 9, 28, 11, 22, 27, 34, 15, 48, 17, 56, 41, 38, 21, 96, 38, 46, 55, 84, 27, 126, 29, 98, 69, 62, 79, 178, 35, 70, 83, 180, 39, 186, 41, 140, 159, 86, 45, 280, 82, 164, 111, 168, 51, 246, 131, 264, 125, 110, 57, 444, 59, 118, 233, 258, 157

Offset: 0

Author

Wesley Ivan Hurt, Jan 16 2022

Keywords

• nonn
• easy

Comments

Sum of the positive differences of the parts in the partitions of n into two parts such that the smaller part divides the larger (see example).

Examples

			a(10) = 14; The partitions of 10 into two parts such that the smaller divides the larger are (1,9), (2,8), and (5,5). The sum of the positive differences of the parts is then (9-1) + (8-2) + (5-5) = 14.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A023645, A032741.

Programs

Mathematica

Join[{0}, Table[n (1 + DivisorSigma[0, n]) - 2*DivisorSigma[1, n], {n, 100}]]

Formula

For n > 0, a(n) = Sum_{d|n, d

For n > 0, a(n) = n*(A000005(n) + 1) - 2*A000203(n).

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