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A114987 Numbers with a 3-almost prime number of prime divisors (counted with multiplicity).

%I A114987 #11 Feb 05 2017 02:52:06
%S A114987 256,384,576,640,864,896,960,1296,1344,1408,1440,1600,1664,1944,2016,
%T A114987 2112,2160,2176,2240,2400,2432,2496,2916,2944,3024,3136,3168,3240,
%U A114987 3264,3360,3520,3600,3648,3712,3744,3968,4000,4096,4160,4374,4416,4536,4704
%N A114987 Numbers with a 3-almost prime number of prime divisors (counted with multiplicity).
%C A114987 This is the 3-almost prime analog of A063989 "numbers with a prime number of prime divisors (counted with multiplicity)" and A110893 "numbers with a semiprime number of prime divisors (counted with multiplicity)." Below 4096, this is identical to 8-almost primes (A014613). Between 4096 and 6144, this is identical to 8-almost primes. Below 262144 this is identical to the union of 8-almost primes (A014613) and 12-almost primes (A069273). Between 262144 and 393216, this is identical to the union of 8-almost primes and 12-almost primes.
%H A114987 Harvey P. Dale, <a href="/A114987/b114987.txt">Table of n, a(n) for n = 1..1000</a>
%F A114987 a(n) such that A001222(A001222(a(n))) = 3. a(n) such that A001222(a(n)) is an element of A014612. a(n) such that bigomega(a(n)) is an element of A014612. Union[8-almost primes (A014613), 12-almost primes (A069273), 18-almost primes (A069279), 20-almost primes (A069281), 27-almost primes]...
%e A114987 a(1) = 256 because 256 = 2^8, which has a 3-almost prime (8) number of prime factors with multiplicity.
%e A114987 a(38) = 4096 because 4096 = 2^12, which has a 3-almost prime (12) number of prime factors with multiplicity.
%t A114987 Select[Range[5000],PrimeOmega[PrimeOmega[#]]==3&] (* _Harvey P. Dale_, Apr 12 2015 *)
%o A114987 (PARI) is(n)=bigomega(bigomega(n))==3 \\ _Charles R Greathouse IV_, Feb 05 2017
%Y A114987 Cf. A001222, A014612, A014613, A069273, A069279, A069281.
%K A114987 easy,nonn
%O A114987 1,1
%A A114987 _Jonathan Vos Post_, Feb 22 2006