A067531 Numbers n such that n - number of divisors of n is a prime.

5, 6, 7, 13, 15, 16, 19, 21, 27, 31, 33, 35, 43, 51, 57, 61, 65, 73, 77, 87, 93, 103, 105, 109, 111, 135, 139, 141, 143, 151, 155, 161, 165, 177, 181, 183, 185, 189, 193, 199, 201, 203, 215, 229, 231, 237, 241, 245, 267, 271, 275, 283, 285, 287, 313, 321, 335

Offset: 1

Author

Amarnath Murthy, Feb 17 2002

Keywords

• easy
• nonn

Comments

Larger of the twin primes (A006512) is a term.

Examples

			51 is a term as d(51) = 4 and 51-4 = 47 is a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005 (number of divisors of n), A006512.

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

Select[Range[400],PrimeQ[#-DivisorSigma[0,#]]&] (* Harvey P. Dale, May 22 2013 *)

Extensions

More terms from James Sellers, Feb 18 2002