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.

A217854 Product of all divisors of n, positive or negative.

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%I A217854 #28 Sep 30 2023 19:33:52
%S A217854 -1,4,9,-64,25,1296,49,4096,-729,10000,121,2985984,169,38416,50625,
%T A217854 -1048576,289,34012224,361,64000000,194481,234256,529,110075314176,
%U A217854 -15625,456976,531441,481890304,841,656100000000,961,1073741824,1185921
%N A217854 Product of all divisors of n, positive or negative.
%C A217854 a(n) is negative iff n is a square.
%H A217854 Hugo Pfoertner, <a href="/A217854/b217854.txt">Table of n, a(n) for n = 1..10000</a>
%F A217854 a(n) = (-n)^tau(n) = (-n)^A000005(n).
%F A217854 a(n) = A158387(n) * A062758(n). - _Andrew Howroyd_, Aug 31 2023
%t A217854 a[n_] := (-n)^DivisorSigma[0, n]; Array[a, 33] (* _Amiram Eldar_, Aug 31 2023 *)
%o A217854 (PARI) a(n) = (-n)^numdiv(n); \\ _Michel Marcus_, Aug 31 2023
%Y A217854 Cf. A000005, A062758, A158387, A363657, A363658.
%K A217854 sign
%O A217854 1,2
%A A217854 _Franklin T. Adams-Watters_, Oct 19 2012