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A222185 Least prime q with q^(p-1) == 1 (mod p^2), where p = A222184(n).

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%I A222185 #6 Apr 30 2017 08:11:18
%S A222185 3,19,53,11,31,53,43,19,79,71,223,257,251,349,307,241,197,503,467,643,
%T A222185 13,127,457,419,487,617,691,2,241,997,821,683,653,421,941,1069,1481,
%U A222185 709,463,461,1153,1381,631,449,1091,277,1993,367,659,151,1657,823,1493,431,1787,2063,1487,59,2389,2131,479,1907,79,173,1151,1831,419,1193,2,3319
%N A222185 Least prime q with q^(p-1) == 1 (mod p^2), where p = A222184(n).
%D A222185 L. E. Dickson, History of the Theory of Numbers, vol. 1, chap. IV.
%H A222185 Giovanni Resta, <a href="/A222185/b222185.txt">Table of n, a(n) for n = 1..10000</a>
%H A222185 Keller and J. Richstein, <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients that are divisible by p</a>
%e A222185 3 is the smallest prime < A222184(1) = 11 such that 11^2 divides 3^(11-1)-1 = 59048 = 121*488, so a(1) = 3.
%t A222185 L = Select[ Prime[ Range[500]], Product[ PowerMod[ Prime[k], # - 1, #^2] - 1, {k, 1, PrimePi[#] - 1}] == 0 &]; Table[  Min[ Select[ Prime[ Range[ PrimePi[L[[n]]] - 1]], PowerMod[#, L[[n]] - 1, L[[n]]^2] == 1 &]], {n, 1, Length[L]}]
%Y A222185 Cf. A001220, A039678, A134307, A143548, A222184.
%K A222185 nonn
%O A222185 1,1
%A A222185 _Jonathan Sondow_, Feb 12 2013