A372305 a(n) = Product_{k=2..n-1} MultiplicativeOrder(k,n) where gcd(k,n)=1.

1, 1, 2, 2, 32, 2, 648, 8, 648, 32, 12500000, 8, 214990848, 648, 2048, 2048, 562949953421312, 648, 11712917736940032, 2048, 3359232, 12500000, 1377791989621882898843648, 128, 5120000000000000000, 214990848, 11712917736940032

Offset: 1

Author

Darío Clavijo, Apr 25 2024

Keywords

• nonn

Comments

All terms are even for n>=3.

Crossrefs

Cf. A000079, A036391, A249435.

Row products of triangle A216327.

Programs

Mathematica

Table[Times @@ Map[MultiplicativeOrder[#, n] &, Select[Range[2, n - 1], CoprimeQ[n, #] &]], {n, 2, 27}] (* Michael De Vlieger, Apr 25 2024 *)

PARI

a(n) = prod(k=2, n-1, if (gcd(k,n)==1, znorder(Mod(k,n)), 1)); \\ Michel Marcus, Apr 26 2024

Python

from sympy import n_order, gcd, prod
a = lambda n: prod(n_order(k,n) for k in range(2, n) if gcd(k,n)==1)
print([a(n) for n in range(1, 28)])