A355643 Numbers k having a divisor d such that d+k/d is prime.

1, 2, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 66, 70, 72, 76, 78, 82, 84, 88, 90, 96, 100, 102, 106, 108, 112, 114, 118, 120, 126, 130, 132, 136, 138, 142, 148, 150, 154, 156, 160, 162, 166, 168, 172, 174, 178, 180, 184, 186, 190, 192, 196, 198, 202, 204, 208

Offset: 1

Author

J. M. Bergot and Robert Israel, Jul 11 2022

Keywords

• nonn

Comments

All terms > 2 are congruent to 0 or 4 (mod 6).

Examples

			a(10) = 24 is a term because 24 = 3*8 with 3+8 = 11 prime.
		

Links

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

Crossrefs

Contains A006093.

Cf. A355644.

Programs

Maple

filter:= proc(n) local F,t;
  F:= select(t -> t^2 <=n, numtheory:-divisors(n));
  ormap(isprime, map(t -> t+n/t, F))
end proc:
select(filter, [$1..300]);

Mathematica

q[n_] := AnyTrue[Divisors[n], PrimeQ[# + n/#] &]; Select[Range[200], q] (* Amiram Eldar, Jul 11 2022 *)

PARI

isok(k) = fordiv(k, d, if (isprime(d+k/d), return(1))); \\ Michel Marcus, Jul 11 2022

Python

from sympy import divisors, isprime
def ok(n): return any(isprime(d+n//d) for d in divisors(n, generator=True))
print([k for k in range(1, 210) if ok(k)]) # Michael S. Branicky, Jul 11 2022