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A074969 Numbers with six distinct prime divisors. 6
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 (list; graph; refs; listen; history; text; internal format)
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. Note that in A001358 (product of two primes), A014612 (product of three primes), A014613 (product of four primes), A014614 (product of five primes), primes are not necessarily distinct, so k-almost primes are the more general class than our d-almost primes with d=k. In the sequence, d-almost primes with d=6 are considered, see also A051270 (d=5), A033993 (d=4), A033992 (d=3), A007774 (d=2). The case d=1 (or k=1) corresponds to primes A000040.

LINKS

Table of n, a(n) for n=1..32.

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

CROSSREFS

Cf. A067885, A001358, A014612, A014613, A014614, A051270, A033993, A033992, A000040.

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

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)