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A383473 Integers k such that d*2^k + 1 is prime for some divisor of k.

%I A383473 #10 May 04 2025 12:40:19
%S A383473 1,2,4,6,8,12,14,15,16,18,25,30,36,51,55,63,66,69,75,81,85,134,141,
%T A383473 162,189,201,209,220,245,276,324,408,438,446,456,534,616,675,693,726,
%U A383473 892,900,1305,1326,1494,1824,2208,2394,2766,2826,3024,3168,3189,3690,3703,3880,3912,3927,4410,4543,4713
%N A383473 Integers k such that d*2^k + 1 is prime for some divisor of k.
%e A383473 6 is in the sequence a term because 3*2^6 + 1 = 193 prime for divisor 3 of k = 6.
%t A383473 q[k_] := AnyTrue[Divisors[k], PrimeQ[# * 2^k +1] &]; Select[Range[4000], q] (* _Amiram Eldar_, Apr 28 2025 *)
%o A383473 (Magma) [k: k in [1..900] | not #[d: d in Divisors(k) | IsPrime(d*2^k+1)] eq 0];
%o A383473 (PARI) isok(k) = fordiv(k, d, if (ispseudoprime(d*2^k+1), return(1))); return(0); \\ _Michel Marcus_, Apr 28 2025
%Y A383473 Supersequence of A005849.
%Y A383473 Cf. A002064, A027750, A382811.
%K A383473 nonn
%O A383473 1,2
%A A383473 _Juri-Stepan Gerasimov_, Apr 27 2025