cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Jonathan Sondow, May 14 2010

Keywords

Comments

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

Examples

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

References

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

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).

Programs

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

Formula

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