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

1,2

Links

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

Formula

Equals {A008578} union {A014612}.

Equals {A037144} minus {A001358}.

Example

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.

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[#]]&]

Prog

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

Crossrefs

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

Subsequence of A037144. - Felix Fröhlich, Jan 15 2018

Sequence in context: A166982 A026422 A026424 * A347453 A229125 A228853

Adjacent sequences: A298204 A298205 A298206 * A298208 A298209 A298210

Keyword

nonn

Author

Gus Wiseman, Jan 14 2018

Status

approved