A384488 Numbers k having a divisor d such that d - k/d is prime.

3, 4, 6, 8, 10, 12, 14, 15, 18, 20, 24, 26, 28, 30, 32, 35, 36, 38, 40, 42, 44, 48, 50, 54, 60, 62, 63, 66, 68, 70, 72, 74, 78, 80, 84, 86, 88, 90, 92, 96, 98, 99, 102, 104, 108, 110, 114, 120, 122, 126, 128, 130, 132, 138, 140, 143, 144, 146, 150, 152, 154, 158, 162, 164, 168, 170, 174, 176, 180

Offset: 1

Author

Juri-Stepan Gerasimov, May 30 2025

Keywords

• nonn

Comments

Presumably, all odd terms are in A000466.

Examples

			a(6) = 12 is a term because 12 = 1*12 with 12 - 1 = 11 prime.
		

Links

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

Crossrefs

Cf. A000466, A005408, A355643. Includes A005563 and 2 * A052147.

Programs

Magma

[k: k in [1..180] | not #[d: d in Divisors (k) | IsPrime(d-(k div d))] eq 0];

Maple

filter:= k -> ormap(d -> d^2 > k and isprime(d - k/d), numtheory:-divisors(k)):
select(filter, [$1..200]); # Robert Israel, Jun 30 2025

Mathematica

A384488Q[k_] := AnyTrue[Divisors[k], PrimeQ[# - k/#] &];
Select[Range[200], A384488Q] (* Paolo Xausa, Jun 30 2025 *)

PARI

isok(k) = fordiv(k, d, if (isprime(d - k/d), return(1))); \\ Michel Marcus, Jun 01 2025