A348951 - OEIS

A348951

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

0, 1, -1, 1, -1, 0, -1, 2, -1, 0, -1, 3, -1, 0, -2, 2, -1, 1, -1, 1, -2, 0, -1, 4, -1, 0, -2, 1, -1, 2, -1, 3, -2, 0, -2, 2, -1, 0, -2, 4, -1, 0, -1, 1, -3, 0, -1, 5, -1, 1, -2, 1, -1, 0, -2, 4, -2, 0, -1, 4, -1, 0, -3, 3, -2, 0, -1, 1, -2, 2, -1, 4, -1, 0, -3, 1, -2, 0, -1, 5

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

OFFSET

1,8

LINKS

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

FORMULA

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

MATHEMATICA

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

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

PROG

(PARI) A348951(n) = sumdiv(n, d, if((d*d)<n, (-1)^(n/d), 0)); \\ Antti Karttunen, Nov 05 2021