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%I #22 May 18 2017 13:17:17
%S 0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,
%U 0,2,0,2,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0
%N Number of primes q < p such that q^(p-1) == 1 (modulo p^2), where p = prime(n).
%C Pairs of prime numbers (q, p) satisfying the conditions in the definition are sometimes called "Wieferich prime pairs" (cf. Mossinghoff, 2009).
%C a(n) > 0 iff p is a term of A222184.
%C First occurrence of k beginning at 0: 1, 5, 70, 1618, 2702, etc. - _Robert G. Wilson v_, May 10 2017
%H M. J. Mossinghoff, <a href="https://doi.org/10.1007/s10623-009-9301-3">Wieferich pairs and Barker sequences</a>, Designs, Codes and Cryptography, Vol. 53, No. 3 (2009), 149-163.
%e For n = 70: prime(70) = 349 and there are two primes q < 349 such that q^(349-1) == 1 (modulo 349^2), namely 223 and 317, so a(70) = 2.
%t f[n_] := Block[{c = 0, p = Prime@ n, q = 2}, While[q < p, If[ PowerMod[q, p - 1, p^2] == 1, c++]; q = NextPrime@q]; c]; Array[f, 105] (* _Robert G. Wilson v_, May 10 2017 *)
%o (PARI) a(n) = my(p=prime(n), i=0); forprime(q=1, p-1, if(Mod(q, p^2)^(p-1)==1, i++)); i
%Y Cf. A222184, A222206 (records).
%K nonn
%O 1,70
%A _Felix Fröhlich_, Apr 30 2017