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%I #14 Jan 08 2020 03:27:56
%S 1093,3511,398945,796797,1592501,1990353,2388205,3183909,3581761,
%T 4377465,5173169,5968873,6165316,10345245,11538801,15119469,16313025,
%U 17506581,18302285,20291545,23076509,23872213,24650731,26657177,29442141,36205625,36974341,37001329,38194885
%N Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.
%C Conjecture: each term is a multiple of a Wieferich prime.
%C Prime numbers in this sequence are the Wieferich primes A001220.
%C Pseudoprime (A001567) terms are 3581761, 5173169, 5968873, 23872213, 36974341, 53711113, ...
%C The terms of A291194 that are not in this sequence are 1194649, 2786057, 3979613, 4775317, 5571021, ....
%H Giovanni Resta, <a href="/A331021/b331021.txt">Table of n, a(n) for n = 1..4184</a> (terms < 10^12)
%e 1093 is a term since gcd(1093^2, 2^1092 - 1) = 1093^2 > 1093.
%t seqQ[n_] := GCD[n^2, PowerMod[2, n - 1, n^2] - 1] > n; Select[Range[10^7], seqQ]
%o (PARI) isok(n) = gcd(n^2, 2^(n-1) - 1) > n; \\ _Michel Marcus_, Jan 07 2020
%Y Cf. A001220, A001567.
%Y Subsequence of A291194.
%K nonn
%O 1,1
%A _Amiram Eldar_ and _Thomas Ordowski_, Jan 07 2020
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