%I
%S 11,43,59,71,79,97,103,137,263,331,349,359,421,433,487,523,653,659,
%T 743,859,863,907,919,983,1069,1087,1091,1093,1163,1223,1229,1279,1381,
%U 1483,1499,1549,1657,1663,1667,1697,1747,1777,1787,1789,1877,1993,2011,2213,2221,2251,2281,2309,2371,2393,2473,2671,2719,2777,2791,2803,2833,2861,3037,3079,3163,3251,3257,3463,3511,3557
%N Primes p such that q^(p1) == 1 (mod p^2) for some prime q < p.
%C Subsequence of A134307; see its interesting heuristics. (What is the analogous heuristic for the present sequence?)
%C The smallest corresponding primes q are A222185.
%D L. E. Dickson, History of the Theory of Numbers, vol. 1, chap. IV.
%H Giovanni Resta, <a href="/A222184/b222184.txt">Table of n, a(n) for n = 1..10000</a>
%H W. Keller and J. Richstein, <a href="http://web.archive.org/web/20091109011757/http://www1.unihamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>.
%F A222185(n)^(a(n)1) == 1 (mod a(n)^2).
%e 3 is a prime < 11, and 11^2 divides 3^(111)1 = 59048 = 121*488, so 11 is a member.
%t Select[ Prime[ Range[500]], Product[ PowerMod[ Prime[k], #  1, #^2]  1, {k, 1, PrimePi[#]  1}] == 0 &]
%o (PARI) lista(nn) = {forprime (p=2, nn, ok = 0; forprime(q=2, p1, if (Mod(q, p^2)^(p1) == 1, ok=1; break);); if (ok, print1(p, ", ")););} \\ _Michel Marcus_, Nov 24 2014
%Y Cf. A001220, A039678, A134307, A143548, A222185.
%K nonn
%O 1,1
%A _Jonathan Sondow_, Feb 11 2013
