A295075 Numbers k such that d + k/d is never prime for any divisor d of k.

3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 25, 26, 27, 29, 31, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 77, 79, 80, 81, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99

Offset: 1

Author

Michel Marcus, Nov 13 2017

Keywords

• nonn

Comments

Numbers k such that A282849(k) = 0.

Links

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

Crossrefs

Cf. A282849 (number of divisors of n such that d + n/d is prime), A080715 (d + n/d is prime for every divisor d of n).

Includes all elements > 2 of A047255.

Programs

Maple

remove(n -> ormap(t -> isprime(t+n/t), numtheory:-divisors(n)), [$1..100]); # Robert Israel, Nov 14 2017

Mathematica

Select[Range@ 100, Function[k, NoneTrue[Divisors@ k, PrimeQ[# + k/#] &]]] (* Michael De Vlieger, Nov 13 2017 *)

PARI

isok(n) = sumdiv(n, d, isprime(d+n/d)) == 0;