A284044 - OEIS

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

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OFFSET

3,3

COMMENTS

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

LINKS

Table of n, a(n) for n=3..89.

EXAMPLE

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.

PROG

(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

CROSSREFS

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

Sequence in context: A134192 A358344 A309342 * A126305 A088431 A254661

Adjacent sequences: A284041 A284042 A284043 * A284045 A284046 A284047

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Apr 02 2017

STATUS

approved