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A222184
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Primes p such that q^(p-1) == 1 (mod p^2) for some prime q < p.
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5
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11, 43, 59, 71, 79, 97, 103, 137, 263, 331, 349, 359, 421, 433, 487, 523, 653, 659, 743, 859, 863, 907, 919, 983, 1069, 1087, 1091, 1093, 1163, 1223, 1229, 1279, 1381, 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
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OFFSET
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1,1
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COMMENTS
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Subsequence of A134307; see its interesting heuristics. (What is the analogous heuristic for the present sequence?)
The smallest corresponding primes q are A222185.
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, vol. 1, chap. IV.
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LINKS
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FORMULA
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A222185(n)^(a(n)-1) == 1 (mod a(n)^2).
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EXAMPLE
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3 is a prime < 11, and 11^2 divides 3^(11-1)-1 = 59048 = 121*488, so 11 is a member.
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MATHEMATICA
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Select[ Prime[ Range[500]], Product[ PowerMod[ Prime[k], # - 1, #^2] - 1, {k, 1, PrimePi[#] - 1}] == 0 &]
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PROG
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(PARI) lista(nn) = {forprime (p=2, nn, ok = 0; forprime(q=2, p-1, if (Mod(q, p^2)^(p-1) == 1, ok=1; break); ); if (ok, print1(p, ", ")); ); } \\ Michel Marcus, Nov 24 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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