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A074969
Numbers with six distinct prime divisors.
13
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 first six primes, 2*3*5*7*11 = 30030. The smallest number with seven distinct prime divisors is product of first seven primes, 2*3*5*7*11*13 = 390390.
LINKS
FORMULA
{n : A001221(n) = 6} . - R. J. Mathar, Jul 07 2012
EXAMPLE
60060 is in the sequence because 60060 = 2^2*3*5*7*11*13 with six distinct prime divisors 2, 3, 5, 7, 11, 13; 87780 is in the sequence 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
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 04 2002
STATUS
approved