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A114987 Numbers with a 3-almost 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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

EXAMPLE

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.

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

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)