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

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

Crossrefs

Cf. A048272, A056924, A113652, A228441, A333809, A348515, A348952, A348953, A348954, A348955, A348956.

Sequence in context: A030528 A077227 A089263 * A369815 A373423 A156135

Adjacent sequences: A348948 A348949 A348950 * A348952 A348953 A348954

Keyword

sign

Author

Ilya Gutkovskiy, Nov 04 2021

Status

approved