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A033992 Numbers that are divisible by exactly three different primes.

%I A033992 #59 Apr 22 2024 08:38:16
%S A033992 30,42,60,66,70,78,84,90,102,105,110,114,120,126,130,132,138,140,150,
%T A033992 154,156,165,168,170,174,180,182,186,190,195,198,204,220,222,228,230,
%U A033992 231,234,238,240,246,252,255,258,260,264,266,270,273,276,280,282,285,286
%N A033992 Numbers that are divisible by exactly three different primes.
%C A033992 This sequence and A000977 are identical through their first 32 terms, but A000977(33) = 210. [Comment edited by _Jon E. Schoenfield_, Dec 30 2014]
%H A033992 T. D. Noe, <a href="/A033992/b033992.txt">Table of n, a(n) for n = 1..1000</a>
%H A033992 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 A033992 omega(a(n)) = A001221(a(n)) = 3. - _Jonathan Vos Post_, Sep 20 2005
%F A033992 a(n) ~ 2n log n / (log log n)^2. - _Charles R Greathouse IV_, Jul 28 2016
%e A033992 220 = 2*2*5*11 is here but 210 = 2*3*5*7 is not; compare A000977.
%p A033992 A033992 := proc(n)
%p A033992 if (nops(numtheory[factorset](n)) = 3) then
%p A033992    RETURN(n)
%p A033992 fi: end:  seq(A033992(n), n=1..500); # _Jani Melik_, Feb 24 2011
%t A033992 Select[Range[300],PrimeNu[#]==3&] (* _Harvey P. Dale_, May 01 2013 *)
%o A033992 (Haskell)
%o A033992 a033992 n = a033992_list !! (n-1)
%o A033992 a033992_list = filter ((== 3) . a001221) [1..]
%o A033992 -- _Reinhard Zumkeller_, May 03 2013
%o A033992 (PARI) is(n)=omega(n)==3 \\ _Charles R Greathouse IV_, Apr 28 2015
%o A033992 (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 A033992 list(lim,pr=3)=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 A033992 A225228 is a subsequence.
%Y A033992 Row 3 of A125666.
%Y A033992 Cf. A000977, A000961, A001221, A112802.
%K A033992 nonn
%O A033992 1,1
%A A033992 _Labos Elemer_