A096226 a(n) is the least exponent k > 1 such that m^k is congruent to m modulo n for all natural numbers m, or a(n) = 1 if no such k exists.

2, 2, 3, 1, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1, 19, 1, 7, 11, 23, 1, 1, 13, 1, 1, 29, 5, 31, 1, 11, 17, 13, 1, 37, 19, 13, 1, 41, 7, 43, 1, 1, 23, 47, 1, 1, 1, 17, 1, 53, 1, 21, 1, 19, 29, 59, 1, 61, 31, 1, 1, 13, 11, 67, 1, 23, 13, 71, 1, 73, 37, 1, 1, 31, 13, 79, 1, 1, 41, 83, 1

Offset

1,1

Comments

If n is squarefree, a(n) = 1+A002322(n) = 1+A011773(n). Otherwise a(n) = 1. a(n) = n iff n is prime.

Links

Table of n, a(n) for n=1..84.

Formula

For squarefree n = p1*p2*...*pj, a(n) = 1+lcm(p1-1, p2-1, ..., pj-1).

Example

a(35) = 13 because 35 divides 1^13-1, 2^13-2, 3^13-3, etc.; but 35 does not divide 2^2-2, 2^3-3, 2^4-2, ..., 2^11-2 or 2^12-2.

Crossrefs

Cf. A002322, A011773.

Sequence in context: A088177 A335917 A028507 * A155980 A309531 A215222

Adjacent sequences: A096223 A096224 A096225 * A096227 A096228 A096229

Keyword

nonn,easy

Author

Franz Vrabec, Aug 09 2004

Extensions

Edited and extended by David Wasserman, Oct 30 2007

Status

approved