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%I #2 Mar 30 2012 19:00:09
%S 1,2,6,90,6720,36960,11642400,283046400,2412984420000,
%T 1140422816332800,1226781977195174400,1863152400854384640000,
%U 5988092802221559085056000,112886540292742916603904000,158983195607776600998537600000000
%N Product of the quadratic nonresidues of prime(n).
%C a(n) == (-1)^((p-1)/2) (mod p), if p = prime(n) is odd.
%D Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398.
%H Rahul Gupta, <a href="http://www.cse.iitd.ernet.in/~sak/courses/ant/notes/ant.pdf">Algorithmic Number Theory, Section 24.5</a>
%F a(n) = (p-1)!/A177860(n), where p = prime(n).
%e The quadratic nonresidues of prime(4) = 7 are 3, 5, and 6, so a(4) = 3*5*6 = 90.
%t Table[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], -1]]], {n, 1, 16}]
%Y A125615 Sum of the quadratic nonresidues of prime(n), A177860 Product of the quadratic residues of prime(n), A177863 Product of the quadratic nonresidues of prime(n) modulo prime(n).
%K easy,nonn
%O 1,2
%A _Jonathan Sondow_, May 14 2010