A382221 - OEIS

A382221

Products of primitive roots when n is 2, 4, p^k, or 2p^k (with p an odd prime), for all other n the value is defined to be 1.

1, 1, 2, 3, 6, 5, 15, 1, 10, 21, 672, 1, 924, 15, 1, 1, 11642400, 55, 163800, 1, 1, 29393, 109681110000, 1, 64411776, 21945, 708400, 1, 5590307923200, 1, 970377408, 1, 1, 644812245, 1, 1, 134088514560000, 11756745, 1, 1, 138960660963091968000, 1

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OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..838

Wikipedia, Primitive root modulo n.

FORMULA

a(n) = A123475(n) if n is prime.

a(A180634(n)) = 1.

a(n) > 1 if n in A033948.

MATHEMATICA

Table[Times @@ PrimitiveRootList[n], {n, 42}] (* Michael De Vlieger, Apr 07 2025 *)

PROG

(Python)

from sympy import gcd, primitive_root, totient

def a(n):

try:

g = primitive_root(n)

except ValueError:

return 1

P = 1

if g:

phi = totient(n)

for k in range(1, phi):

if gcd(k, phi) == 1:

P *= pow(g, k, n)

return P

print([a(n) for n in range(1, 43)])

CROSSREFS

Cf. A033948, A121380, A123475, A180634.

Sequence in context: A225652 A136183 A100211 * A071257 A067392 A066449

Adjacent sequences: A382218 A382219 A382220 * A382222 A382223 A382224

KEYWORD

nonn

AUTHOR

Darío Clavijo, Mar 27 2025

STATUS

approved