A137230 Composite numbers that are divisible by the number of their prime factors (counted with multiplicity).

4, 6, 10, 12, 14, 16, 18, 22, 24, 26, 27, 30, 34, 36, 38, 40, 42, 45, 46, 56, 58, 60, 62, 63, 66, 74, 75, 78, 80, 82, 84, 86, 88, 94, 96, 99, 100, 102, 104, 105, 106, 114, 117, 118, 120, 122, 132, 134, 136, 138, 140, 142, 144, 146, 147, 152, 153, 156, 158, 165, 166

Offset: 1

Author

William A. Tedeschi, Mar 07 2008

Keywords

• nonn

Comments

k is a term iff {k == 0 (mod BigOmega(k)) and k NOT prime}.

This sequence is obtained from A074946 by excluding all primes from that sequence.

Examples

			k = 3; not a term because not a prime.
k = 4; a term because satisfies both k == 0 (mod bigomega(k)) and k NOT prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Factor.

Crossrefs

Cf. A001222, A002808, A074946.

Programs

Mathematica

Select[Range[200], CompositeQ[#] && Divisible[#, PrimeOmega[#]]&] (* Jean-François Alcover, Nov 11 2016 *)

PARI

isok(c) = (c>1) && !isprime(c) && !(c % bigomega(c)); \\ Michel Marcus, Feb 28 2023

Extensions

Edited by Michel Marcus, Feb 28 2023