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

1,1

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.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Row 6 of A125666.

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

Sequence in context: A106771 A184502 A285655 * A066765 A067885 A285615

Adjacent sequences: A074966 A074967 A074968 * A074970 A074971 A074972

Keyword

nonn

Author

Zak Seidov, Oct 04 2002

Status

approved