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A348952
a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).
5
0, 1, -1, 1, -1, 2, -1, 0, -1, 2, -1, 1, -1, 2, -2, 0, -1, 3, -1, 1, -2, 2, -1, 0, -1, 2, -2, 1, -1, 4, -1, -1, -2, 2, -2, 2, -1, 2, -2, 0, -1, 4, -1, 1, -3, 2, -1, -1, -1, 3, -2, 1, -1, 4, -2, 0, -2, 2, -1, 2, -1, 2, -3, -1, -2, 4, -1, 1, -2, 4, -1, 0, -1, 2, -3, 1, -2, 4, -1, -1
OFFSET
1,6
LINKS
FORMULA
G.f.: Sum_{k>=1} x^(k*(k + 1)) / (1 + x^k).
For p odd prime, a(p) = a(p^2) = -1. - Bernard Schott, Nov 22 2021
MATHEMATICA
Table[-DivisorSum[n, (-1)^(# + n/#) &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) A348952(n) = -sumdiv(n, d, if((d*d)<n, (-1)^(d + (n/d)), 0)); \\ Antti Karttunen, Nov 05 2021
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 04 2021
STATUS
approved