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 A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k. 2
 1093, 3511, 398945, 796797, 1592501, 1990353, 2388205, 3183909, 3581761, 4377465, 5173169, 5968873, 6165316, 10345245, 11538801, 15119469, 16313025, 17506581, 18302285, 20291545, 23076509, 23872213, 24650731, 26657177, 29442141, 36205625, 36974341, 37001329, 38194885 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: each term is a multiple of a Wieferich prime. Prime numbers in this sequence are the Wieferich primes A001220. Pseudoprime (A001567) terms are 3581761, 5173169, 5968873, 23872213, 36974341, 53711113, ... The terms of A291194 that are not in this sequence are 1194649, 2786057, 3979613, 4775317, 5571021, .... LINKS Giovanni Resta, Table of n, a(n) for n = 1..4184 (terms < 10^12) EXAMPLE 1093 is a term since gcd(1093^2, 2^1092 - 1) = 1093^2 > 1093. MATHEMATICA seqQ[n_] := GCD[n^2, PowerMod[2, n - 1, n^2] - 1] > n; Select[Range[10^7], seqQ] PROG (PARI) isok(n) = gcd(n^2, 2^(n-1) - 1) > n; \\ Michel Marcus, Jan 07 2020 CROSSREFS Cf. A001220, A001567. Subsequence of A291194. Sequence in context: A001220 A265630 A291194 * A270833 A273471 A266829 Adjacent sequences:  A331018 A331019 A331020 * A331022 A331023 A331024 KEYWORD nonn AUTHOR Amiram Eldar and Thomas Ordowski, Jan 07 2020 STATUS approved

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Last modified July 25 11:31 EDT 2021. Contains 346289 sequences. (Running on oeis4.)