A069233 Numbers k such that there is exactly 1 prime p satisfying the inequality k < p < k + tau(k)^2 where tau(k) = A000005(k).

3, 5, 11, 17, 29, 41, 49, 59, 71, 101, 107, 111, 115, 121, 137, 149, 169, 179, 191, 197, 201, 202, 203, 205, 206, 227, 239, 269, 281, 287, 289, 291, 295, 311, 314, 319, 321, 347, 361, 403, 419, 431, 461, 469, 471, 505, 521, 526, 527, 569, 599, 617, 622, 623

Offset: 1

Author

Benoit Cloitre, Apr 13 2002

Keywords

• easy
• nonn

Comments

Numbers k such that A069230(k) = 1. - Amiram Eldar, Jan 29 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A049591, A069230, A069231, A069232.

Programs

Mathematica

q[k_] := Count[k + Range[1, DivisorSigma[0, k]^2 - 1], ?PrimeQ] == 1; Select[Range[640], q] (* _Amiram Eldar, Jan 29 2025 *)

PARI

isok(n) = #select(x->isprime(x), vector(numdiv(n)^2-1, k, k+n)) == 1; \\ Michel Marcus, Jun 18 2017