A382811 Integers k such that d*2^k - 1 is prime for some divisor d of k.

2, 3, 4, 5, 6, 7, 10, 12, 13, 16, 17, 18, 19, 21, 28, 30, 31, 36, 42, 46, 54, 60, 61, 63, 75, 81, 88, 89, 99, 102, 104, 106, 107, 108, 115, 123, 126, 127, 132, 133, 204, 214, 216, 225, 249, 264, 270, 286, 304, 306, 324, 330, 342, 352, 362, 384, 390

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 15 2025

Keywords

• nonn

Examples

			4 is in the sequence because 2*2^4 - 1 = 31 is prime for divisor d = 2 of k = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..161

Crossrefs

Supersequence of A000043, A002234.

Programs

Magma

[k: k in [1..400] | not #[d: d in Divisors(k) | IsPrime(d*2^k-1)] eq 0];

Maple

filter:= proc(k) ormap(d -> isprime(d*2^k-1),numtheory:-divisors(k)) end proc:
select(filter, [$1..700]); # Robert Israel, Apr 25 2025

Mathematica

q[k_] := AnyTrue[Divisors[k], PrimeQ[#*2^k - 1] &]; Select[Range[400], q] (* Amiram Eldar, Apr 16 2025 *)

PARI

isok(k) = fordiv(k, d, if (ispseudoprime(d*2^k-1), return(1))); \\ Michel Marcus, Apr 16 2025