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A074969
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Numbers with six distinct prime divisors.
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5
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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; internal format)
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OFFSET
| 1,1
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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.
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EXAMPLE
| 60060 is OK because 60060=2^2*3*5*7*11 with six distinct prime divisors 2, 3, 5, 7, 11, 13; 87780 is OK because 87780=2^2*3*5*11*19 with six distinct prime divisors 2, 3, 5, 7, 11, 19.
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MATHEMATICA
| Select[Range[0, 5*8! ], Length[FactorInteger[ # ]]==6&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 22 2010]
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CROSSREFS
| Cf. A001358, A014612, A014613, A014614, A051270, A033993, A033992, A000040.
Sequence in context: A183852 A106771 A184502 * A066765 A067885 A072940
Adjacent sequences: A074966 A074967 A074968 * A074970 A074971 A074972
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 04 2002
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