A177861 Product of the quadratic nonresidues of prime(n).

1, 2, 6, 90, 6720, 36960, 11642400, 283046400, 2412984420000, 1140422816332800, 1226781977195174400, 1863152400854384640000, 5988092802221559085056000, 112886540292742916603904000, 158983195607776600998537600000000

Offset

1,2

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)!/A177860(n), where p = prime(n).

Example

The quadratic nonresidues of prime(4) = 7 are 3, 5, and 6, so a(4) = 3*5*6 = 90.

Mathematica

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

Crossrefs

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).

Sequence in context: A128265 A002432 A087277 * A218151 A343021 A007188

Adjacent sequences: A177858 A177859 A177860 * A177862 A177863 A177864

Keyword

easy,nonn

Author

Jonathan Sondow, May 14 2010

Status

approved