A348953 - OEIS

A348953

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

0, 1, -1, 1, -1, 3, -1, -1, -1, 3, -1, 2, -1, 3, -4, -1, -1, 6, -1, 3, -4, 3, -1, -2, -1, 3, -4, 3, -1, 11, -1, -5, -4, 3, -6, 6, -1, 3, -4, 0, -1, 12, -1, 3, -9, 3, -1, -8, -1, 8, -4, 3, -1, 12, -6, 2, -4, 3, -1, 5, -1, 3, -11, -5, -6, 12, -1, 3, -4, 15, -1, 0, -1, 3, -9, 3, -8, 12, -1, -8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

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

FORMULA

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

MATHEMATICA

Table[-DivisorSum[n, (-1)^(# + n/#) # &, # < Sqrt[n] &], {n, 1, 80}]

nmax = 80; CoefficientList[Series[Sum[k x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PROG

(PARI) A348953(n) = -sumdiv(n, d, if((d*d)<n, d*(-1)^(d + (n/d)), 0)); \\ Antti Karttunen, Nov 05 2021