

A166718


Numbers with at most 4 prime factors (counted with multiplicity)


2



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, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76
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OFFSET

1,2


COMMENTS

Complement of A046304, A001222(a(n)) <= 4.
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]
Subset of the 5free numbers (numbers where each exponent in the prime factorization is <=4).  R. J. Mathar, Aug 08 2012


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
James Maynard, Bounded length intervals containing two primes and an almostprime, arXiv:1205.5020v1 [math.NT], May 22 2012


FORMULA

UNION of A000040, A001358, A014612, and A014613.  R. J. Mathar, Aug 08 2012


EXAMPLE

88 = 2*2*2*11 is in the sequence since it has 4 prime factors
72 = 2*2*2*3*3 is not in the sequence since it has 5 prime factors


MATHEMATICA

Select[Range[100], PrimeOmega[#]<= 4 &] (* G. C. Greubel, May 24 2016 *)


PROG

(PARI) isA166718(n) = (bigomega(n) <= 4)


CROSSREFS

Cf. A046304, A001222
For numbers with at most n prime factors: n=1: A000040, n=2: A037143, n=3: A037144, n=5: A166719
Sequence in context: A114086 A257333 A090110 * A132016 A032513 A272323
Adjacent sequences: A166715 A166716 A166717 * A166719 A166720 A166721


KEYWORD

easy,nonn


AUTHOR

Michael B. Porter, Oct 20 2009


STATUS

approved



