A348952 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).

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

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

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

Crossrefs

Cf. A048272, A056924, A228441, A258453, A305152, A333809, A348515, A348951, A348953, A348954, A348955, A348956.

Sequence in context: A143519 A344606 A341592 * A307778 A029376 A276790

Adjacent sequences: A348949 A348950 A348951 * A348953 A348954 A348955

Keyword

sign

Author

Ilya Gutkovskiy, Nov 04 2021

Status

approved