A158340 Composite numbers k such that (number of prime factors of k, counted with multiplicity) + (number of divisors of k) is a prime.

4, 8, 9, 25, 27, 30, 32, 36, 42, 49, 64, 66, 70, 72, 78, 100, 102, 105, 108, 110, 114, 121, 125, 130, 138, 154, 165, 169, 170, 174, 180, 182, 186, 190, 195, 196, 200, 222, 225, 230, 231, 238, 243, 246, 252, 255, 256, 258, 266, 273, 282, 285, 286, 289, 290, 300

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 16 2009, Nov 14 2009

Keywords

• nonn

Examples

			4 is a term: 4 = 2*2 has 2 prime factors (counted with multiplicity) and 3 divisors (1, 2, and 4), and 2 + 3 = 5 (a prime).
8 is a term: 8 = 2*2*2 has 3 prime factors and 4 divisors (1, 2, 4, and 8), and 3 + 4 = 7 (a prime).
9 is a term: 9 = 3*3 has 2 prime factors and 3 divisors (1, 3, and 9), and 2 + 3 = 5 (a prime).
		

Crossrefs

Cf. A000040, A002808, A035004.

Extensions

Corrected (148 replaced with 138) by R. J. Mathar, May 19 2010