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

1,1

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

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Row 4 of A125666.

Cf. A000977, A002110, A001221.

Sequence in context: A119427 A127424 A074159 * A350373 A046386 A379762

Adjacent sequences: A033990 A033991 A033992 * A033994 A033995 A033996

Keyword

nonn,easy

Author

Labos Elemer

Status

approved