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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
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
Subsequence of A291194.
Sequence in context: A265630 A355545 A291194 * A270833 A273471 A266829
KEYWORD
nonn
AUTHOR
Amiram Eldar and Thomas Ordowski, Jan 07 2020
STATUS
approved