cp's OEIS Frontend

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

%I A348952 #21 Aug 20 2025 10:58:00
%S A348952 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,
%T A348952 -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,
%U A348952 -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
%N A348952 a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d).
%H A348952 Antti Karttunen, <a href="/A348952/b348952.txt">Table of n, a(n) for n = 1..20000</a>
%F A348952 G.f.: Sum_{k>=1} x^(k*(k + 1)) / (1 + x^k).
%F A348952 For p odd prime, a(p) = a(p^2) = -1. - _Bernard Schott_, Nov 22 2021
%F A348952 a(n) = (A010052(n) - A228441(n))/2. - _Ridouane Oudra_, Aug 14 2025
%F A348952 a(n) = A010052(n) - A305152(n). - _Ridouane Oudra_, Aug 20 2025
%t A348952 Table[-DivisorSum[n, (-1)^(# + n/#) &, # < Sqrt[n] &], {n, 1, 80}]
%t A348952 nmax = 80; CoefficientList[Series[Sum[x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A348952 (PARI) A348952(n) = -sumdiv(n,d,if((d*d)<n,(-1)^(d + (n/d)),0)); \\ _Antti Karttunen_, Nov 05 2021
%Y A348952 Cf. A048272, A056924, A228441, A258453, A305152, A333809, A348515, A348951, A348953, A348954, A348955, A348956, A010052.
%K A348952 sign
%O A348952 1,6
%A A348952 _Ilya Gutkovskiy_, Nov 04 2021