A033993 Numbers that are divisible by exactly four different primes.

210, 330, 390, 420, 462, 510, 546, 570, 630, 660, 690, 714, 770, 780, 798, 840, 858, 870, 910, 924, 930, 966, 990, 1020, 1050, 1092, 1110, 1122, 1140, 1155, 1170, 1190, 1218, 1230, 1254, 1260, 1290, 1302, 1320, 1326, 1330, 1365, 1380, 1386, 1410, 1428

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

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

Examples

			The 4th primorial is the first term of this sequence: A002110(4) = 210.
		

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.

Crossrefs

Row 4 of A125666.

Cf. A000977, A002110, A001221.

Programs

Mathematica

Select[Range[1500], Length[FactorInteger[#]] == 4 &] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2010 *)

PARI

is(n)=omega(n)==4 \\ Charles R Greathouse IV, Sep 17 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=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

Formula

a(n) has exactly 4 distinct prime factors. omega(a(n)) = A001221(a(n)) = 4. - Jonathan Vos Post, Sep 21 2005