A358816 Numbers k such that d + k/d is prime for any unitary divisor d of k.

1, 2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 52, 58, 60, 70, 72, 78, 82, 88, 100, 102, 108, 112, 130, 148, 162, 172, 190, 192, 196, 198, 210, 228, 232, 240, 250, 256, 268, 270, 280, 310, 312, 316, 330, 352, 358, 372, 378, 382, 388, 396, 400, 408, 432, 442, 448

Offset: 1

Author

Amiram Eldar, Dec 02 2022

Keywords

• nonn

Comments

A unitary divisor d of k is a number d such that d|k and gcd(d, k/d) = 1.

A080715 is the subsequence of the squarefree terms of this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Unitary Divisor.
• Wikipedia, Unitary divisor.

Crossrefs

Cf. A005117, A077610, A080715.

Subsequence of A006093.

Programs

Mathematica

q[n_] := AllTrue[Select[Divisors[n], #^2 < n && CoprimeQ[#, n/#] &], PrimeQ[# + n/#] &]; Select[Prime[Range[90]] - 1, q]

PARI

is(n) = fordiv(n, d, if(d < n^2 && gcd(d, n/d) == 1 && !isprime(d+n/d), return(0))); return(1);