A284044 Largest positive k among all primes p < n such that n^(p-1) == 1 (mod p^k).

1, 1, 2, 1, 2, 2, 3, 2, 1, 1, 2, 1, 1, 1, 4, 3, 3, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 5, 1, 2, 1, 2, 2, 1, 2, 3, 3, 2, 2, 2, 2, 1, 2, 4, 2, 2, 1, 3, 2, 3, 1, 3, 1, 1, 2, 2, 2, 2, 2, 6, 1, 2, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 4, 4, 4, 1, 1, 2, 1, 1, 1, 3

Offset: 3

Author

Felix Fröhlich, Apr 02 2017

Keywords

• nonn

Comments

a(n) > 1 iff A255920(n) > 0, i.e., iff n is a term of A273786.

Examples

			For n = 7: the maximal exponents k in the congruence 7^(p-1) == 1 (mod p^k) for p = 2, 3, 5 are 1, 1, 2, respectively. Since 2 is the largest exponent among that list, a(7) = 2.
		

Crossrefs

Cf. A255920, A258045, A268310, A273786, A278701, A282902.

Programs

PARI

a(n) = my(r=1); forprime(p=1, n-1, my(k=1); while(1, if(Mod(n, p^k)^(p-1)!=1, k--; break, k++)); if(k > r, r=k)); r