A116660 Integers in both sequences A075658 and A067028.

56, 60, 84, 90, 104, 126, 132, 135, 140, 150, 152, 156, 184, 189, 196, 198, 204, 220, 224, 225, 228, 234, 240, 248, 260, 276, 294, 296, 297, 306, 308, 315, 330, 336, 340, 342, 344, 348, 350, 351, 360, 364, 372, 375, 376, 380, 414, 416, 424, 441, 444, 459

Offset: 1

Author

Leroy Quet, Feb 21 2006

Keywords

• nonn

Comments

It could be argued that 1 should also be included in the sequence, if 0 is considered to be a composite, since the number of prime divisors (counted with multiplicity) of 1 and the sum of 1's distinct prime divisors are both 0.

Examples

			60 = 2^2 *3^1 *5^1. Both the number of prime divisors (counted with multiplicity), 2+1+1 = 4 and the sum of the distinct prime divisors, 2+3+5 = 10, are composite. So 60 is in the sequence.
		

Links

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

Crossrefs

Cf. A075658, A067028, A116661.

Programs

Mathematica

Select[Range[460], CompositeQ[Plus @@ (f = FactorInteger[#])[[;; , 1]]] && CompositeQ[Plus @@ f[[;; , 2]]] &] (* Amiram Eldar, Nov 14 2019 *)

Extensions

More terms from R. J. Mathar, Aug 31 2007