A393401 Numbers k such that k*2^d + 1 is composite for any of its divisors d.

7, 13, 17, 19, 25, 27, 31, 32, 37, 38, 43, 46, 47, 49, 55, 59, 61, 62, 66, 67, 71, 73, 79, 80, 82, 85, 87, 91, 92, 93, 94, 97, 101, 103, 104, 106, 107, 109, 110, 115, 118, 121, 122, 123, 124, 127, 133, 136, 137, 139, 143, 145, 147, 149, 151, 152, 157, 159, 161

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

7 is a term because 7*2^1 + 1 = 15 and 7*2^7 + 1 = 897 are composites for divisors 1 and 7 of 7.

Maple

filter:= proc(k) andmap(d -> not isprime(k*2^d+1), NumberTheory:-Divisors(k)) end proc:
select(filter, [$1..200]); # Robert Israel, Mar 29 2026

Mathematica

q[k_] := AllTrue[Divisors[k], CompositeQ[k*2^# + 1] &]; Select[Range[161], q] (* Amiram Eldar, Feb 24 2026 *)

Prog

(Magma) [k: k in [1..200] | #[d: d in Divisors(k) | IsPrime(k*2^d+1)] eq 0];
(PARI) isok(k) = fordiv(k, d, if (isprime(k*2^d+1), return(0))); 1; \\ Michel Marcus, Feb 18 2026

Crossrefs

Cf. A002808, A005849, A027750, A053176, A383475.

Sequence in context: A118942 A067656 A166602 * A079697 A079695 A396685

Adjacent sequences: A393398 A393399 A393400 * A393402 A393403 A393404

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 13 2026

Status

approved