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Search: id:A064708
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| A064708 |
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Initial term of run of (at least) n consecutive numbers with just 2 distinct prime factors. |
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+0
5
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OFFSET
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1,1
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COMMENT
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It can be shown by an application of Mihailescu's theorem that a(12) does not exist, since then there would be two 3-smooth numbers close together (it suffices to check up to 2*3^3).
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REFERENCES
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Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag 81 (2008), 235-248. [From T. D. Noe (noe(AT)sspectra.com), Oct 13 2008]
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EXAMPLE
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6 = 2*3; 14 = 2*7 and 15 = 3*5; 20 = 2^2*5, 21 = 3*7 and 22 = 2*11; 33 = 3*11, 34 = 2*17, 35 = 5*7 and 36 = (2*3)^2; etc.
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CROSSREFS
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Cf. A064709.
Sequence in context: A048747 A101567 A123267 this_sequence A064709 A118129 A046712
Adjacent sequences: A064705 A064706 A064707 this_sequence A064709 A064710 A064711
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KEYWORD
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nonn,fini
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 13 2001
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EXTENSIONS
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If a(9) exists, it is greater than 10^30. - Don Reble (djr(AT)nk.ca), Mar 02 2003
If a(9) exists, it is greater than 10^3000. - Charles R Greathouse IV, Apr 22 2009
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