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A350801
a(n) = n*(tau(n) + 1) - 2*sigma(n) for n>=1, with a(0)=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).
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 16 2022
STATUS
approved