cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325939 Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k).

This page as a plain text file.
%I A325939 #11 Sep 20 2019 21:12:58
%S A325939 0,1,-1,2,-1,1,-1,3,-2,1,-1,3,-1,1,-3,4,-1,1,-1,3,-3,1,-1,5,-2,1,-3,3,
%T A325939 -1,1,-1,5,-3,1,-3,4,-1,1,-3,5,-1,1,-1,3,-5,1,-1,7,-2,1,-3,3,-1,1,-3,
%U A325939 5,-3,1,-1,5,-1,1,-5,6,-3,1,-1,3,-3,1,-1,7,-1,1,-5,3,-3,1,-1,7
%N A325939 Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k).
%C A325939 Number of even divisors of n minus number of odd strong divisors of n (i.e. odd divisors > 1).
%H A325939 Antti Karttunen, <a href="/A325939/b325939.txt">Table of n, a(n) for n = 1..65537</a>
%F A325939 G.f.: Sum_{k>=2} (-1)^k * x^k / (1 - x^k).
%F A325939 a(n) = Sum_{d|n, d>1} (-1)^d.
%F A325939 a(n) = 1 - A048272(n).
%t A325939 nmax = 80; CoefficientList[Series[Sum[x^(2 k)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A325939 Table[DivisorSum[n, (-1)^# &, # > 1 &], {n, 1, 80}]
%o A325939 (PARI) A325939(n) = sumdiv(n, d, if(1==d,0,((-1)^d))); \\ _Antti Karttunen_, Sep 20 2019
%Y A325939 Cf. A032741, A048272, A075997 (partial sums), A325937.
%K A325939 sign,look
%O A325939 1,4
%A A325939 _Ilya Gutkovskiy_, Sep 09 2019