A033992 Numbers that are divisible by exactly three different primes.
30, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 195, 198, 204, 220, 222, 228, 230, 231, 234, 238, 240, 246, 252, 255, 258, 260, 264, 266, 270, 273, 276, 280, 282, 285, 286
Offset: 1
Keywords
Examples
220 = 2*2*5*11 is here but 210 = 2*3*5*7 is not; compare A000977.
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Hans Montanus and Ron Westdijk, Cellular Automation and Binomials, Green Blue Mathematics (2022), p. 90.
Programs
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Haskell
a033992 n = a033992_list !! (n-1) a033992_list = filter ((== 3) . a001221) [1..] -- Reinhard Zumkeller, May 03 2013
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Maple
A033992 := proc(n) if (nops(numtheory[factorset](n)) = 3) then RETURN(n) fi: end: seq(A033992(n), n=1..500); # Jani Melik, Feb 24 2011
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Mathematica
Select[Range[300],PrimeNu[#]==3&] (* Harvey P. Dale, May 01 2013 *)
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PARI
is(n)=omega(n)==3 \\ Charles R Greathouse IV, Apr 28 2015
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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) 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
Formula
omega(a(n)) = A001221(a(n)) = 3. - Jonathan Vos Post, Sep 20 2005
a(n) ~ 2n log n / (log log n)^2. - Charles R Greathouse IV, Jul 28 2016
Comments