A335022 a(n) = Sum_{d|n, 1 < d < n} (-1)^(d + 1) * d.

0, 0, 0, -2, 0, 1, 0, -6, 3, 3, 0, -9, 0, 5, 8, -14, 0, 4, 0, -11, 10, 9, 0, -29, 5, 11, 12, -13, 0, 5, 0, -30, 14, 15, 12, -30, 0, 17, 16, -39, 0, 9, 0, -17, 32, 21, 0, -69, 7, 18, 20, -19, 0, 13, 16, -49, 22, 27, 0, -61, 0, 29, 40, -62, 18, 17, 0, -23, 26, 21, 0, -98, 0, 35, 48, -25

Offset: 1

Author

Ilya Gutkovskiy, May 19 2020

Keywords

• sign

Comments

Difference between the sum of the odd nontrivial divisors of n and the sum of the even nontrivial divisors of n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A002129, A048050, A058344, A335021.

Programs

Mathematica

Table[DivisorSum[n, (-1)^(# + 1) # &, 1 < # < n &], {n, 1, 76}]
nmax = 76; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(2 k)/(1 - x^k), {k, 2, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, if ((d>1) && (dMichel Marcus, May 20 2020

Formula

G.f.: Sum_{k>=2} (-1)^(k + 1) * k * x^(2*k) / (1 - x^k).