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%I #13 Apr 03 2021 08:43:08
%S 7957,23377,30889,35333,42799,49981,60787,91001,129889,150851,162193,
%T 164737,241001,249841,253241,256999,280601,318361,387731,452051,
%U 481573,556169,580337,617093,665333,722201,838861,877099,1016801,1251949,1252697,1325843,1507963
%N Numbers k such that 2^(k-1) == 1 (mod k) and lpf(k)-1 does not divide k-1.
%C Are there infinitely many such pseudoprimes?
%H Amiram Eldar, <a href="/A316906/b316906.txt">Table of n, a(n) for n = 1..10000</a>
%e 7957 = 73*109 is pseudoprime and 72 does not divide 7956.
%e 30889 = 17*23*79 is pseudoprime and 16 does not divide 30888.
%t Select[Range[760000] 2 + 1, PowerMod[2, #-1, #] == 1 && Mod[#-1, FactorInteger[#][[1, 1]] - 1] > 0 &] (* _Giovanni Resta_, Jul 16 2018 *)
%Y Subsequence of A001567.
%Y Cf. A020639 (lpf(n)).
%K nonn
%O 1,1
%A _Thomas Ordowski_, Jul 16 2018
%E a(8)-a(33) from _Giovanni Resta_, Jul 16 2018