A050704 Composite numbers k with the property that k minus the sum of the prime factors of k is prime.

8, 9, 10, 12, 14, 15, 20, 21, 26, 28, 33, 35, 38, 39, 40, 44, 48, 51, 54, 56, 62, 65, 68, 69, 76, 77, 80, 86, 88, 91, 93, 95, 96, 111, 112, 116, 122, 123, 124, 129, 133, 136, 146, 148, 152, 159, 161, 176, 188, 189, 198, 201, 203, 206, 209, 210, 213, 215, 217, 218

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn
• nice

Comments

Prime factors are totaled with multiplicity, e.g., 8 = 2*2*2 so the sum of the prime factors of 8 is 6. - Harvey P. Dale, Jun 14 2011

Examples

			E.g., 161 = 7*23; 161 - (7 + 23) = 161 - 30 = 131, which is prime.
		

Links

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

Crossrefs

Cf. A050703-A050710.

Programs

Mathematica

 Select[Range[250],CompositeQ[#]&&PrimeQ[#-Total[Times@@@ FactorInteger[ #]]]&] (* Harvey P. Dale, Jun 14 2011 *)