

A298207


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


2



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
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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(n1)) 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 * A229125 A228853 A141832
Adjacent sequences: A298204 A298205 A298206 * A298208 A298209 A298210


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 14 2018


STATUS

approved



