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A232195 Product of distinct squares in Z_n (mod n), without the factor 0.

%I A232195 #31 Apr 01 2021 14:54:41
%S A232195 0,1,1,1,4,0,1,4,1,0,1,0,12,0,0,4,16,0,1,0,0,0,1,0,24,0,9,0,28,0,1,0,
%T A232195 0,0,0,0,36,0,0,0,40,0,1,0,0,0,1,0,1,0,0,0,52,0,0,0,0,0,1,0,60,0,0,0,
%U A232195 0,0,1,0,0,0,1,0,72,0,0,0,0,0,1,0,0,0,1,0
%N A232195 Product of distinct squares in Z_n (mod n), without the factor 0.
%C A232195 Up to n = 10000 a(n) is divisible by 4 except for the values 1 and 9 (a(27)).
%H A232195 Robert Israel, <a href="/A232195/b232195.txt">Table of n, a(n) for n = 1..10000</a>
%F A232195 From _Robert Israel_, Apr 01 2021: (Start)
%F A232195 a(n) = 0 if n is in A024619, or if n = p^d with p > 3 prime and d >= 3, or if n = 2^d with d >= 5, or if n = 3^d with d >= 4.
%F A232195 a(p) = a(p^2) = 1 if p is in A002145.
%F A232195 a(p) = p-1 and a(p^2) = p^2-1 if p is in A002144.
%F A232195 (End)
%p A232195 A232195:= proc (n) options operator, arrow; modp(convert(`minus`({seq(modp(k^2, n), k = 1 .. n-1)}, {0}), `*`), n) end proc; seq(A232195(i), i = 1 .. 30);
%o A232195 (PARI) a(n) = if (n==1, 0, lift(vecprod(Set(select(x->(issquare(x) && (x!=0)), vector(n-1, k, Mod(k, n))))))); \\ _Michel Marcus_, Apr 01 2021
%Y A232195 A071782 describes the sum of distinct squares in Z_n (mod n).
%Y A232195 A000224 describes the number of distinct squares in Z_n (mod n).
%Y A232195 Cf. A002144, A002145, A024619.
%K A232195 nonn
%O A232195 1,5
%A A232195 _Martin Schellenberg_, Nov 20 2013