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A033993 Numbers that are divisible by exactly four different primes.

%I A033993 #33 Apr 22 2024 09:38:07
%S A033993 210,330,390,420,462,510,546,570,630,660,690,714,770,780,798,840,858,
%T A033993 870,910,924,930,966,990,1020,1050,1092,1110,1122,1140,1155,1170,1190,
%U A033993 1218,1230,1254,1260,1290,1302,1320,1326,1330,1365,1380,1386,1410,1428
%N A033993 Numbers that are divisible by exactly four different primes.
%C A033993 For a(n) < 30030 = 2 * 3 * 5 * 7 * 11 * 13 this is identical to "numbers with a semiprime number of distinct prime factors." - _Jonathan Vos Post_, Sep 21 2005
%H A033993 T. D. Noe, <a href="/A033993/b033993.txt">Table of n, a(n) for n = 1..1000</a>
%H A033993 Hans Montanus and Ron Westdijk, <a href="https://greenbluemath.nl/wp-content/uploads/2024/03/Cellular-Automation-and-Binomials.pdf">Cellular Automation and Binomials</a>, Green Blue Mathematics (2022), p. 90.
%F A033993 a(n) has exactly 4 distinct prime factors. omega(a(n)) = A001221(a(n)) = 4. - _Jonathan Vos Post_, Sep 21 2005
%e A033993 The 4th primorial is the first term of this sequence: A002110(4) = 210.
%t A033993 Select[Range[1500], Length[FactorInteger[#]] == 4 &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2010 *)
%o A033993 (PARI) is(n)=omega(n)==4 \\ _Charles R Greathouse IV_, Sep 17 2015
%o A033993 (PARI) A246655(lim)=my(v=List(primes([2,lim\=1]))); for(e=2,logint(lim,2), forprime(p=2,sqrtnint(lim,e), listput(v,p^e))); Set(v)
%o A033993 list(lim,pr=4)=if(pr==1, return(A246655(lim))); my(v=List(),pr1=pr-1,mx=prod(i=1,pr1,prime(i))); forprime(p=prime(pr),lim\mx, my(u=list(lim\p,pr1)); for(i=1,#u,listput(v,p*u[i]))); Set(v) \\ _Charles R Greathouse IV_, Feb 03 2023
%Y A033993 Row 4 of A125666.
%Y A033993 Cf. A000977, A002110, A001221.
%K A033993 nonn,easy
%O A033993 1,1
%A A033993 _Labos Elemer_