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%I #28 Jul 19 2023 07:38:56
%S 30030,39270,43890,46410,51870,53130,60060,62790,66990,67830,71610,
%T 72930,78540,79170,81510,82110,84630,85470,87780,90090,91770,92820,
%U 94710,98670,99330,101010,102102,103530,103740,106260,106590,108570
%N Numbers with six distinct prime divisors.
%C 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.
%H Amiram Eldar, <a href="/A074969/b074969.txt">Table of n, a(n) for n = 1..10000</a>
%F {n : A001221(n) = 6} . - _R. J. Mathar_, Jul 07 2012
%e 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.
%t Select[Range[0,5*8! ],Length[FactorInteger[ # ]]==6&] (* _Vladimir Joseph Stephan Orlovsky_, Apr 22 2010 *)
%o (PARI) is(n)=omega(n)==6 \\ _Charles R Greathouse IV_, Jun 19 2016
%o (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)
%o 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
%Y Row 6 of A125666.
%Y Cf. A067885, A001358, A014612, A014613, A014614.
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 04 2002
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