

A114987


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


1



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
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OFFSET

1,1


COMMENTS

This is the 3almost 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 8almost primes (A014613). Between 4096 and 6144, this is identical to 8almost primes. Below 262144 this is identical to the union of 8almost primes (A014613) and 12almost primes (A069273). Between 262144 and 393216, this is identical to the union of 8almost primes and 12almost primes.


LINKS

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


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[8almost primes (A014613), 12almost primes (A069273), 18almost primes (A069279), 20almost primes (A069281), 27almost primes]...


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A001222, A014612, A014613, A069273, A069279, A069281.
Sequence in context: A186473 A046309 A036332 * A046310 A115176 A299156
Adjacent sequences: A114984 A114985 A114986 * A114988 A114989 A114990


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 22 2006


STATUS

approved



