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 A345460 Odd numbers k with (k-1)/2 not prime such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1. 0

%I

%S 1,3,9,13,17,19,31,33,37,43,65,79,115,129,187,223,367,403,535,763,835

%N Odd numbers k with (k-1)/2 not prime such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1.

%C Are there only finitely many such numbers? No more terms below 2217.

%C For those numbers k, if k <> 2^m + 1, then k == 1 (mod 6).

%t q[k_] := AllTrue[FactorInteger[2^(k - 1) - 1][[;; , 1]], Divisible[k - 1, # - 1] || Divisible[# - 1, k - 1] &]; Select[Range[1, 230, 2], ! PrimeQ[(# - 1)/2] && q[#] &]

%Y Cf. A334797 (see comments section).

%K nonn,more

%O 1,2

%A _Amiram Eldar_ and _Thomas Ordowski_, Jun 20 2021

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Last modified December 1 20:01 EST 2021. Contains 349430 sequences. (Running on oeis4.)