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Composite numbers that are divisible by the number of their prime factors (counted with multiplicity).
3

%I #20 Feb 28 2023 09:45:43

%S 4,6,10,12,14,16,18,22,24,26,27,30,34,36,38,40,42,45,46,56,58,60,62,

%T 63,66,74,75,78,80,82,84,86,88,94,96,99,100,102,104,105,106,114,117,

%U 118,120,122,132,134,136,138,140,142,144,146,147,152,153,156,158,165,166

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

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

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

%H Amiram Eldar, <a href="/A137230/b137230.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>.

%e k = 3; not a term because not a prime.

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

%t Select[Range[200], CompositeQ[#] && Divisible[#, PrimeOmega[#]]&] (* _Jean-François Alcover_, Nov 11 2016 *)

%o (PARI) isok(c) = (c>1) && !isprime(c) && !(c % bigomega(c)); \\ _Michel Marcus_, Feb 28 2023

%Y Cf. A001222, A002808, A074946.

%K nonn

%O 1,1

%A _William A. Tedeschi_, Mar 07 2008

%E Edited by _Michel Marcus_, Feb 28 2023