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

256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4096, 4160, 4374, 4416, 4536, 4704

Offset: 1

Author

Jonathan Vos Post, Feb 22 2006

Keywords

• easy
• nonn

Comments

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.

Examples

			a(1) = 256 because 256 = 2^8, which has a 3-almost prime (8) number of prime factors with multiplicity.
a(38) = 4096 because 4096 = 2^12, which has a 3-almost prime (12) number of prime factors with multiplicity.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001222, A014612, A014613, A069273, A069279, A069281.

Programs

Mathematica

Select[Range[5000],PrimeOmega[PrimeOmega[#]]==3&] (* Harvey P. Dale, Apr 12 2015 *)

PARI

is(n)=bigomega(bigomega(n))==3 \\ Charles R Greathouse IV, Feb 05 2017

Formula

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]...