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

Offset: 1

Author

Ilya Gutkovskiy, Nov 04 2021

Keywords

• sign
• changed

Links

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

Crossrefs

Cf. A000593, A046897, A070039, A109506, A333810, A348608, A348951, A348952, A348954, A348955, A348956, A037213.

Programs

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

PARI

A348953(n) = -sumdiv(n,d,if((d*d)Antti Karttunen, Nov 05 2021

Formula

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

a(n) = A037213(n) - A348608(n). - Ridouane Oudra, Aug 21 2025