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

1,1

Comments

This sequence and A000977 are identical through their first 32 terms, but A000977(33) = 210. [Comment edited by Jon E. Schoenfield, Dec 30 2014]

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.

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

Example

220 = 2*2*5*11 is here but 210 = 2*3*5*7 is not; compare A000977.

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

Mathematica

Select[Range[300], PrimeNu[#]==3&] (* Harvey P. Dale, May 01 2013 *)

Prog

(Haskell)
a033992 n = a033992_list !! (n-1)
a033992_list = filter ((== 3) . a001221) [1..]
-- Reinhard Zumkeller, May 03 2013
(PARI) is(n)=omega(n)==3 \\ Charles R Greathouse IV, Apr 28 2015
(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

Crossrefs

A225228 is a subsequence.

Row 3 of A125666.

Cf. A000977, A000961, A001221, A112802.

Sequence in context: A299991 A000977 A214195 * A360525 A308127 A349794

Adjacent sequences: A033989 A033990 A033991 * A033993 A033994 A033995

Keyword

nonn,changed

Author

Labos Elemer

Status

approved