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 A046306 Numbers that are divisible by exactly 6 primes with multiplicity. 54

%I

%S 64,96,144,160,216,224,240,324,336,352,360,400,416,486,504,528,540,

%T 544,560,600,608,624,729,736,756,784,792,810,816,840,880,900,912,928,

%U 936,992,1000,1040,1104,1134,1176,1184,1188,1215,1224,1232,1260,1312,1320

%N Numbers that are divisible by exactly 6 primes with multiplicity.

%C Also called 6-almost primes. Products of exactly 6 primes (not necessarily distinct). Any 6-almost prime can be represented in several ways as a product of two 3-almost primes A014612 and in several ways as a product of three semiprimes A001358. - _Jonathan Vos Post_, Dec 11 2004

%H T. D. Noe, <a href="/A046306/b046306.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Product p_i^e_i with Sum e_i = 6.

%F a(n) ~ 120n log n / (log log n)^5. - _Charles R Greathouse IV_, May 06 2013

%t Select[Range[500], Plus @@ Last /@ FactorInteger[ # ] == 6 &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2008 *)

%t Select[Range[1400],PrimeOmega[#]==6&] (* _Harvey P. Dale_, May 21 2012 *)

%o (PARI) is(n)=bigomega(n)==6 \\ _Charles R Greathouse IV_, Mar 21 2013

%Y Cf. A046305, A120047 (number of 6-almost primes <= 10^n).

%Y Cf. A101605, A101606.

%Y Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), this sequence (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), A069274 (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - _Jason Kimberley_, Oct 02 2011

%K nonn

%O 1,1

%A _Patrick De Geest_, Jun 15 1998

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