A074969 Numbers with six distinct prime divisors.

30030, 39270, 43890, 46410, 51870, 53130, 60060, 62790, 66990, 67830, 71610, 72930, 78540, 79170, 81510, 82110, 84630, 85470, 87780, 90090, 91770, 92820, 94710, 98670, 99330, 101010, 102102, 103530, 103740, 106260, 106590, 108570

Offset: 1

Author

Zak Seidov, Oct 04 2002

Keywords

• nonn

Comments

The smallest number with six distinct prime divisors is the product of the first six primes, 2*3*5*7*11 = 30030.

The smallest number with seven distinct prime divisors is the product of the first seven primes, 2*3*5*7*11*13 = 390390.

Examples

			60060 is a term because 60060 = 2^2*3*5*7*11*13 with six distinct prime divisors 2, 3, 5, 7, 11, 13
87780 is a term because 87780 = 2^2*3*5*7*11*19 with six distinct prime divisors 2, 3, 5, 7, 11, 19.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Row 6 of A125666.

Cf. A067885, A001358, A014612, A014613, A014614.

Programs

Mathematica

Select[Range[0,5*8! ],Length[FactorInteger[ # ]]==6&] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2010 *)

PARI

is(n)=omega(n)==6 \\ Charles R Greathouse IV, Jun 19 2016

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=6)=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

{n : A001221(n) = 6} . - R. J. Mathar, Jul 07 2012