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A033992 Numbers that are divisible by exactly three different primes. 33

%I

%S 30,42,60,66,70,78,84,90,102,105,110,114,120,126,130,132,138,140,150,

%T 154,156,165,168,170,174,180,182,186,190,195,198,204,220,222,228,230,

%U 231,234,238,240,246,252,255,258,260,264,266,270,273,276,280,282,285

%N Numbers that are divisible by exactly three different primes.

%C 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 T. D. Noe, <a href="/A033992/b033992.txt">Table of n, a(n) for n = 1..1000</a>

%F omega(a(n)) = A001221(a(n)) = 3. - _Jonathan Vos Post_, Sep 20 2005

%F a(n) ~ 2n log n / (log log n)^2. - _Charles R Greathouse IV_, Jul 28 2016

%e 220=2*2*5*11 is here but 210 is not; compare A000977.

%p A033992 := proc(n)

%p if (nops(numtheory[factorset](n)) = 3) then

%p RETURN(n)

%p fi: end: seq(A033992(n), n=1..500); # _Jani Melik_, Feb 24 2011

%t Select[Range[0,6! ],Length[FactorInteger[ # ]]==3&] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2010 *)

%t Select[Range[300],PrimeNu[#]==3&] (* _Harvey P. Dale_, May 01 2013 *)

%o (Haskell)

%o a033992 n = a033992_list !! (n-1)

%o a033992_list = filter ((== 3) . a001221) [1..]

%o -- _Reinhard Zumkeller_, May 03 2013

%o (PARI) is(n)=omega(n)==3 \\ _Charles R Greathouse IV_, Apr 28 2015

%o (PARI) list(lim)=my(v=List(),pq); forprime(p=2, lim\6, forprime(q=2, min(p-2, lim\p\2), pq=p*q; forprime(r=2, min(q-1, lim\r), listput(

%Y Cf. A000977, A007774, A000961, A033993, A051270, A112802.

%Y Cf. A225228 (subsequence).

%K nonn

%O 1,1

%A _Labos Elemer_

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Last modified January 18 19:46 EST 2020. Contains 331030 sequences. (Running on oeis4.)