A067532 Numbers k such that k + number of divisors of k is a prime.

1, 3, 4, 5, 11, 15, 17, 27, 29, 33, 39, 41, 55, 57, 59, 64, 69, 71, 85, 93, 100, 101, 105, 107, 123, 133, 137, 145, 149, 159, 165, 175, 177, 179, 187, 189, 191, 197, 219, 227, 231, 235, 237, 239, 245, 247, 253, 255, 259, 265, 267, 269, 273, 275, 281, 285, 303

Offset: 1

Author

Amarnath Murthy, Feb 17 2002

Keywords

• easy
• nonn

Comments

Smaller of the twin primes (A001359) is a term.

Examples

			a(1) = 1 (1+d(1) = 1+1 = 2 = prime).
a(2) = 3 (3+d(3) = 3+2 = 5 = prime).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001359, A067531.

Programs

Maple

with(numtheory): for n from 3 to 500 do if isprime(n+tau(n)) then printf(`%d,`,n) fi:od: # James Sellers, Feb 18 2002

Mathematica

a067532[n_] := Select[Range[n], PrimeQ[# + DivisorSigma[0, #]] &]; a067532[303] (* Michael De Vlieger, Dec 22 2014 *)

PARI

isok(k) = isprime(k + numdiv(k)); \\ Amiram Eldar, Jan 27 2025

Extensions

More terms from James Sellers, Feb 18 2002

Sequence corrected by Juri-Stepan Gerasimov, Oct 18 2009

Offset corrected by N. J. A. Sloane, Oct 21 2009

Corrected by Charles R Greathouse IV, Mar 19 2010