cp's OEIS Frontend

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

%I A298207 #24 Jan 30 2018 17:29:45
%S A298207 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,
%T A298207 47,50,52,53,59,61,63,66,67,68,70,71,73,75,76,78,79,83,89,92,97,98,99,
%U A298207 101,102,103,105,107,109,110,113,114,116,117,124,125,127,130
%N A298207 Numbers that are a product of zero, one, or three (not necessarily distinct) prime numbers.
%H A298207 Alois P. Heinz, <a href="/A298207/b298207.txt">Table of n, a(n) for n = 1..10000</a>
%F A298207 Equals {A008578} union {A014612}.
%F A298207 Equals {A037144} minus {A001358}.
%e A298207 1 is a product of zero primes so is in the sequence.
%e A298207 6 = 2 * 3 is a product of two primes so is not in the sequence.
%e A298207 12 = 2 * 2 * 3 is a product of three primes so is in the sequence.
%p A298207 a:= proc(n) option remember; local k; for k
%p A298207       from 1+`if`(n=1, 0, a(n-1)) while not
%p A298207       numtheory[bigomega](k) in {0, 1, 3} do od; k
%p A298207     end:
%p A298207 seq(a(n), n=1..70);  # _Alois P. Heinz_, Jan 15 2018
%t A298207 Select[Range[200],MemberQ[{0,1,3},PrimeOmega[#]]&]
%o A298207 (PARI) is(n) = my(v=[0, 1, 3]); #setintersect([bigomega(n)], v)==1 \\ _Felix Fröhlich_, Jan 15 2018
%Y A298207 Cf. A000040, A001358, A001399, A008578, A014591, A014612, A026424, A028260, A298120, A298204, A298205.
%Y A298207 Subsequence of A037144. - _Felix Fröhlich_, Jan 15 2018
%K A298207 nonn
%O A298207 1,2
%A A298207 _Gus Wiseman_, Jan 14 2018