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

0,5

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).

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

Formula

For n > 0, a(n) = Sum_{d|n, d<n} (n - 2d).

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A256662 A055944 A331633 * A073740 A239956 A077320

Adjacent sequences: A350798 A350799 A350800 * A350802 A350803 A350804

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 16 2022

Status

approved