A166718 Numbers with at most 4 prime factors (counted with multiplicity).

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

Offset: 1

Author

Michael B. Porter, Oct 20 2009

Keywords

• easy
• nonn

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 5-free numbers (numbers where each exponent in the prime factorization is <=4). - R. J. Mathar, Aug 08 2012

Examples

			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
		

Links

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

Crossrefs

Cf. A046304, A001222

For numbers with at most n prime factors: n=1: A000040, n=2: A037143, n=3: A037144, n=5: A166719

Programs

Mathematica

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

PARI

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

Formula

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