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%I #18 May 25 2016 22:03:26
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,
%U 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76
%N Numbers with at most 4 prime factors (counted with multiplicity)
%C Complement of A046304, A001222(a(n)) <= 4.
%C Maynard shows there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and a number with at most 4 prime factors [_Jonathan Vos Post_, May 23 2012]
%C Subset of the 5-free numbers (numbers where each exponent in the prime factorization is <=4). - _R. J. Mathar_, Aug 08 2012
%H G. C. Greubel, <a href="/A166718/b166718.txt">Table of n, a(n) for n = 1..10000</a>
%H James Maynard, <a href="http://arxiv.org/abs/1205.5020">Bounded length intervals containing two primes and an almost-prime</a>, arXiv:1205.5020v1 [math.NT], May 22 2012
%F UNION of A000040, A001358, A014612, and A014613. - _R. J. Mathar_, Aug 08 2012
%e 88 = 2*2*2*11 is in the sequence since it has 4 prime factors
%e 72 = 2*2*2*3*3 is not in the sequence since it has 5 prime factors
%t Select[Range[100],PrimeOmega[#]<= 4 &] (* _G. C. Greubel_, May 24 2016 *)
%o (PARI) isA166718(n) = (bigomega(n) <= 4)
%Y Cf. A046304, A001222
%Y For numbers with at most n prime factors: n=1: A000040, n=2: A037143, n=3: A037144, n=5: A166719
%K easy,nonn
%O 1,2
%A _Michael B. Porter_, Oct 20 2009
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