A372651 a(n) is the product of the distinct nonzero quadratic residues of n.

1, 1, 1, 1, 4, 12, 8, 4, 28, 1080, 540, 36, 12960, 44352, 2160, 36, 1797120, 524160, 22619520, 2880, 1088640, 4790016000, 465813504, 6912, 5096577024, 8115883776000, 5477472000, 2419200, 267346759680000, 124104960000, 216218419200000, 244800, 143187264000

Offset

1,5

Links

Table of n, a(n) for n=1..33.

Formula

a(n) mod n = A232195(n).

a(n) = Product_{k=1..n} A046071(n,k).

Prog

(Python)
from sympy import prod
def a(n):
  k, QS = 0, []
  for i in range((n >> 1) + 1):
    if k > 0: QS.append(k)
    k += (i << 1) + 1
    k %= n
  return prod(set(QS))
print([a(n) for n in range(1, 34)])
(Python)
from math import prod
from sympy.ntheory.residue_ntheory import quadratic_residues
def A372651(n): return prod(r for r in quadratic_residues(n) if r) # Chai Wah Wu, May 30 2024
(PARI) a(n) = my(list=List()); for (i=1, n-1, if (issquare(Mod(i, n)), listput(list, i))); vecprod(Vec(list)); \\ Michel Marcus, May 28 2024

Crossrefs

Cf. A046071, A105612, A165909, A230366, A232195.

Sequence in context: A335914 A377047 A331054 * A361192 A310569 A145046

Adjacent sequences: A372648 A372649 A372650 * A372652 A372653 A372654

Keyword

nonn

Author

Darío Clavijo, May 27 2024

Status

approved