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A177860 Product of the quadratic residues of prime(n). 2

%I

%S 1,1,4,8,540,12960,1797120,22619520,465813504,267346759680000,

%T 216218419200000,199658024013127680000,136256285631578112000000,

%U 12446179270879850496000000,34611344543529418987929600

%N Product of the quadratic residues 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)!/A177861(n), where p = prime(n).

%e The quadratic residues of prime(4) = 7 are 1, 2, and 4, so a(4) = 1*2*4 = 8.

%t Table[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]], {n, 1, 16}]

%Y Cf. A076409 Sum of the quadratic residues of prime(n), A177861 Product of the quadratic nonresidues of prime(n), A163366 Product of the quadratic residues of prime(n) modulo prime(n).

%K easy,nonn

%O 1,3

%A _Jonathan Sondow_, May 14 2010

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Last modified August 6 17:06 EDT 2020. Contains 336255 sequences. (Running on oeis4.)