login
A372651
a(n) is the product of the distinct nonzero quadratic residues of n.
3
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
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
KEYWORD
nonn
AUTHOR
Darío Clavijo, May 27 2024
STATUS
approved