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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.
14

%I #12 Sep 27 2015 09:40:48

%S 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,

%T 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,

%U 1,2,0,2,1,2,2,1,1,1,3,2,2,0,0,1,0,0,0

%N 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.

%H Felix Fröhlich, <a href="/A255920/b255920.txt">Table of n, a(n) for n = 2..9999</a>

%t 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 *)

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

%Y Cf. A242830.

%K nonn

%O 2,16

%A _Felix Fröhlich_, Mar 11 2015