A273786 Numbers n where a prime p < n exists such that n^(p-1) == 1 (mod p^2), i.e., such that p is a base-n Wieferich prime.

5, 7, 8, 9, 10, 13, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 89, 91, 93, 94

Offset

1,1

Comments

Numbers n such that A255920(n) > 0.

Complement of A255921. - Felix Fröhlich, Dec 03 2020

Links

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

Example

The prime 5 satisfies 24^(5-1) == 1 (mod 5^2) and 5 < 24, so 24 is a term of the sequence.

Mathematica

Select[Range@ 94, Function[n, Count[Prime@ Range@ PrimePi@ n, p_ /; Mod[n^(p - 1), p^2] == 1] > 0]] (* Michael De Vlieger, May 30 2016 *)

Prog

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

Crossrefs

Cf. A255920, A255921, A273785.

Sequence in context: A242273 A261917 A111339 * A255922 A241028 A171097

Adjacent sequences: A273783 A273784 A273785 * A273787 A273788 A273789

Keyword

nonn

Author

Felix Fröhlich, May 30 2016

Status

approved