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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.
3

%I #14 Dec 07 2020 01:48:27

%S 5,7,8,9,10,13,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,35,37,

%T 38,40,41,42,43,44,45,46,48,49,50,51,53,54,55,57,60,61,62,63,64,65,67,

%U 68,69,70,71,73,74,75,76,77,78,79,80,81,82,85,89,91,93,94

%N 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.

%C Numbers n such that A255920(n) > 0.

%C Complement of A255921. - _Felix Fröhlich_, Dec 03 2020

%H Felix Fröhlich, <a href="/A273786/b273786.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

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

%Y Cf. A255920, A255921, A273785.

%K nonn

%O 1,1

%A _Felix Fröhlich_, May 30 2016