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.

A071323 Alternating sum of all divisors of n; divisors nondecreasing, starting with 1.

This page as a plain text file.
%I A071323 #31 Mar 12 2025 00:13:18
%S A071323 1,-1,-2,3,-4,-4,-6,-5,7,-6,-10,-8,-12,-8,-12,11,-16,-13,-18,-12,-16,
%T A071323 -12,-22,-16,21,-14,-20,-18,-28,-22,-30,-21,-24,-18,-32,25,-36,-20,
%U A071323 -28,-24,-40,-32,-42,-30,-36,-24,-46,-32,43
%N A071323 Alternating sum of all divisors of n; divisors nondecreasing, starting with 1.
%H A071323 Harvey P. Dale, <a href="/A071323/b071323.txt">Table of n, a(n) for n = 1..1000</a>
%H A071323 Mihai Caragiu and Kaleb Swieringa, <a href="https://doi.org/10.17654/0972555524006">On the alternating sum-of-divisors</a>, JP Journal of Algebra, Number Theory and Applications, 63(2) (2024), 97-110 (page 3, expression 4).
%F A071323 a(n) = A071324(n) > 0 iff n square (iff A000005(n) is even), a(A000290(n)) > 0.
%F A071323 For primes p, a(p) = 1 - p.
%F A071323 From _Shreyansh Jaiswal_, Mar 04 2025: (Start)
%F A071323 a(n) = -A071324(n) < 0 iff n is nonsquare.
%F A071323 abs(a(n)) = A071324(n). (End)
%e A071323 Divisors of 20 are {1,2,4,5,10,20}, therefore a(20) = 1 - 2 + 4 - 5 + 10 - 20 = -12.
%t A071323 Table[Total[Times@@@Partition[Riffle[Divisors[n],{1,-1},{2,-1,2}],2]],{n,50}] (* _Harvey P. Dale_, Nov 05 2014 *)
%Y A071323 Cf. A000203, A071321, A071324.
%K A071323 sign
%O A071323 1,3
%A A071323 _Reinhard Zumkeller_, May 18 2002