A393401 - OEIS

%I #28 Mar 29 2026 08:59:24

%S 7,13,17,19,25,27,31,32,37,38,43,46,47,49,55,59,61,62,66,67,71,73,79,

%T 80,82,85,87,91,92,93,94,97,101,103,104,106,107,109,110,115,118,121,

%U 122,123,124,127,133,136,137,139,143,145,147,149,151,152,157,159,161

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

%H Robert Israel, <a href="/A393401/b393401.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p filter:= proc(k) andmap(d -> not isprime(k*2^d+1), NumberTheory:-Divisors(k)) end proc:

%p select(filter, [$1..200]); # _Robert Israel_, Mar 29 2026

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

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

%o (PARI) isok(k) = fordiv(k, d, if (isprime(k*2^d+1), return(0))); 1; \\ _Michel Marcus_, Feb 18 2026

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

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 13 2026