A381924 Multiplicative order of n mod prime(n).

1, 2, 4, 3, 5, 12, 16, 6, 11, 28, 30, 9, 40, 21, 46, 13, 29, 60, 33, 7, 24, 13, 41, 88, 48, 100, 34, 106, 54, 7, 63, 26, 136, 23, 74, 75, 39, 9, 166, 86, 178, 5, 95, 192, 196, 99, 105, 222, 113, 228, 29, 34, 120, 250, 256, 262, 67, 270, 46, 8, 47, 292, 153, 155, 312

Offset: 1

Author

Giorgos Kalogeropoulos, Mar 12 2025

Keywords

• nonn

Comments

a(n) is the least k such that prime(n) divides n^k-1.

Examples

			a(12) = 9 because the multiplicative order of 12 mod prime(12) is 9.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3500

Crossrefs

Cf. A226295, A014664, A091185 (n^(-1) mod prime(n)).

Programs

Magma

[Order(n, NthPrime(n)) : n in [1..65]]; // Vincenzo Librandi, Mar 25 2025

Mathematica

Table[MultiplicativeOrder[n,Prime[n]],{n,65}]

PARI

a(n) = znorder(Mod(n, prime(n))); \\ Michel Marcus, Mar 12 2025

Formula

If n is a primitive root modulo prime(n), a(n) = prime(n) - 1.