A273786 -id:A273786 - cp's OEIS frontend

A255921 Bases b for which no primes p with p < b exist such that p is a base-b Wieferich prime.

2, 3, 4, 6, 11, 12, 14, 15, 16, 20, 34, 36, 39, 47, 52, 56, 58, 59, 66, 72, 83, 84, 86, 87, 88, 90, 92, 95, 96, 102, 103, 104, 106, 108, 111, 114, 119, 123, 135, 139, 140, 142, 144, 156, 159, 160, 162, 167, 171, 175, 180, 183, 186, 187, 194, 198, 200, 203, 204

Offset: 1

Felix Fröhlich, Mar 11 2015

nonn

Numbers b such that A255920(b) = 0.

Complement of A273786. - Felix Fröhlich, Dec 03 2020

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Cf. A255920, A255922, A255923, A255924, A255925, A273786.

is(b) = forprime(p=1, b-1, if(Mod(b, p^2)^(p-1)==1, return(0))); 1

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

Original entry on oeis.org

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

Felix Fröhlich, Apr 02 2017

nonn

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

			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.

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

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

cp's OEIS Frontend

A255921 Bases b for which no primes p with p < b exist such that p is a base-b Wieferich prime.

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