A298207 Numbers that are a product of zero, one, or three (not necessarily distinct) prime numbers.

1, 2, 3, 5, 7, 8, 11, 12, 13, 17, 18, 19, 20, 23, 27, 28, 29, 30, 31, 37, 41, 42, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 66, 67, 68, 70, 71, 73, 75, 76, 78, 79, 83, 89, 92, 97, 98, 99, 101, 102, 103, 105, 107, 109, 110, 113, 114, 116, 117, 124, 125, 127, 130

Offset: 1

Author

Gus Wiseman, Jan 14 2018

Keywords

• nonn

Examples

			1 is a product of zero primes so is in the sequence.
6 = 2 * 3 is a product of two primes so is not in the sequence.
12 = 2 * 2 * 3 is a product of three primes so is in the sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A001399, A008578, A014591, A014612, A026424, A028260, A298120, A298204, A298205.

Subsequence of A037144. - Felix Fröhlich, Jan 15 2018

Programs

Maple

a:= proc(n) option remember; local k; for k
      from 1+`if`(n=1, 0, a(n-1)) while not
      numtheory[bigomega](k) in {0, 1, 3} do od; k
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jan 15 2018

Mathematica

Select[Range[200],MemberQ[{0,1,3},PrimeOmega[#]]&]

PARI

is(n) = my(v=[0, 1, 3]); #setintersect([bigomega(n)], v)==1 \\ Felix Fröhlich, Jan 15 2018

Formula

Equals {A008578} union {A014612}.

Equals {A037144} minus {A001358}.