A371531 a(n) is the multiplicative order of A053669(n) modulo n.

1, 1, 2, 2, 4, 2, 3, 2, 6, 4, 10, 2, 12, 6, 4, 4, 8, 6, 18, 4, 6, 5, 11, 2, 20, 3, 18, 6, 28, 4, 5, 8, 10, 16, 12, 6, 36, 18, 12, 4, 20, 6, 14, 10, 12, 11, 23, 4, 21, 20, 8, 6, 52, 18, 20, 6, 18, 28, 58, 4, 60, 30, 6, 16, 12, 10, 66, 16, 22, 12, 35, 6, 9, 18, 20

Offset

1,3

Links

Table of n, a(n) for n=1..75.

Formula

a(2k+1) = A002326(k) for k >= 1.

a(2k) = ord(A284723(k), 2k).

Mathematica

a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; MultiplicativeOrder[p, n]]; Array[a, 75] (* Amiram Eldar, Mar 26 2024 *)

Prog

(Python)
from sympy.ntheory.residue_ntheory import n_order
from sympy import nextprime
def a(n):
  if n == 1: return 1
  if n & 1 == 1: return n_order(2, n)
  p = 2
  while n % p == 0:
    p = nextprime(p)
  return n_order(p, n)
print([a(n) for n in range(1, 76)])
(PARI) f(n) = forprime(p=2, , if(n%p, return(p))); \\ A053669
a(n) = znorder(Mod(f(n), n)); \\ Michel Marcus, Mar 26 2024

Crossrefs

Cf. A002326, A053669, A284723.

Sequence in context: A328059 A123674 A363219 * A238745 A092607 A221861

Adjacent sequences: A371528 A371529 A371530 * A371532 A371533 A371534

Keyword

nonn,new

Author

Darío Clavijo, Mar 26 2024

Status

approved