A291194 -id:A291194 - cp's OEIS frontend

A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.

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

Amiram Eldar and Thomas Ordowski, Jan 07 2020

nonn

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, ....

			1093 is a term since gcd(1093^2, 2^1092 - 1) = 1093^2 > 1093.

Giovanni Resta, Table of n, a(n) for n = 1..4184 (terms < 10^12)

Cf. A001220, A001567.

Subsequence of A291194.

seqQ[n_] := GCD[n^2, PowerMod[2, n - 1, n^2] - 1] > n; Select[Range[10^7], seqQ]

isok(n) = gcd(n^2, 2^(n-1) - 1) > n; \\ Michel Marcus, Jan 07 2020

cp's OEIS Frontend

A331021 Numbers k such that gcd(k^2, 2^(k-1) - 1) > k.

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