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

1, 1, 4, 8, 540, 12960, 1797120, 22619520, 465813504, 267346759680000, 216218419200000, 199658024013127680000, 136256285631578112000000, 12446179270879850496000000, 34611344543529418987929600

Offset

1,3

Comments

a(n) == (-1)^((p+1)/2) (mod p), if p = prime(n) is odd.

References

Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398.

Links

Table of n, a(n) for n=1..15.

Rahul Gupta, Algorithmic Number Theory, Section 24.5

Formula

a(n) = (p-1)!/A177861(n), where p = prime(n).

Example

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

Mathematica

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

Crossrefs

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).

Sequence in context: A136386 A260726 A308553 * A013443 A013442 A013441

Adjacent sequences: A177857 A177858 A177859 * A177861 A177862 A177863

Keyword

easy,nonn

Author

Jonathan Sondow, May 14 2010

Status

approved