A394706 Numbers k such that k*2^d - 1 is nonprime for any of its divisors d.

1, 5, 11, 13, 14, 17, 23, 25, 29, 35, 41, 43, 44, 46, 47, 53, 58, 59, 61, 62, 65, 67, 71, 73, 74, 77, 83, 86, 88, 89, 94, 95, 101, 102, 103, 107, 109, 113, 118, 119, 125, 127, 128, 131, 134, 137, 143, 146, 148, 149, 151, 155, 161, 163, 164, 167, 172, 173, 178, 179, 181, 183, 185, 191, 193, 194, 197

Offset

1,2

Links

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

Example

5 is a term because 5*2^1 - 1 = 9 and 5*2^5 - 1 = 157 are composites for divisors 1 and 5 of 5.

Maple

filter:= proc(n)
     andmap(d -> not isprime(n*2^d-1), NumberTheory:-Divisors(n))
end proc:
select(filter, [$1..1000]); # Robert Israel, May 07 2026

Mathematica

q[k_] := AllTrue[Divisors[k], !PrimeQ[k*2^# - 1] &]; Select[Range[200], q] (* Amiram Eldar, Mar 30 2026 *)

Prog

(Magma) [k: k in [1..200] | #[d: d in Divisors(k) | IsPrime(k*2^d - 1)] eq 0];

Crossrefs

Superset of A307390.

Cf. A002808, A382811, A393401.

Sequence in context: A357995 A104215 A392611 * A287123 A227146 A251965

Adjacent sequences: A394703 A394704 A394705 * A394707 A394708 A394709

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 29 2026

Status

approved