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A177860
Product of the quadratic residues of prime(n).
2
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.
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Sondow, May 14 2010
STATUS
approved