A255920 Number of primes p with p < n such that n^(p-1) == 1 (mod p^2) i.e., number of Wieferich primes to base n less than n.

0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 2, 3, 0, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 3, 1, 1, 0, 2, 0, 0, 1, 1, 2, 2, 1, 2, 0, 2, 3, 2, 1, 2, 0, 2, 1, 2, 2, 1, 1, 1, 3, 2, 2, 0, 0, 1, 0, 0, 0

Offset

2,16

Links

Felix Fröhlich, Table of n, a(n) for n = 2..9999

Mathematica

f[n_] := Block[{p = Complement[Prime@ Range@ PrimePi@ n, First /@ FactorInteger@ n]}, Select[p, Divisible[n^(# - 1) - 1, #^2] &]]; Length /@ Table[f@ n, {n, 2, 120}] (* Michael De Vlieger, Sep 24 2015 *)

Prog

(PARI) for(n=2, 120, i=0; forprime(p=1, n, if(Mod(n, p^2)^(p-1)==1, i++)); print1(i, ", "))

Crossrefs

Cf. A242830.

Sequence in context: A187096 A340146 A340143 * A160115 A139365 A071479

Adjacent sequences: A255917 A255918 A255919 * A255921 A255922 A255923

Keyword

nonn

Author

Felix Fröhlich, Mar 11 2015

Status

approved