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A129912
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Numbers that are products of distinct primorial numbers (see A002110).
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6
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1, 2, 6, 12, 30, 60, 180, 210, 360, 420, 1260, 2310, 2520, 4620, 6300, 12600, 13860, 27720, 30030, 37800, 60060, 69300, 75600, 138600, 180180, 360360, 415800, 485100, 510510, 831600, 900900, 970200, 1021020, 1801800, 2910600, 3063060, 5405400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjecture: every odd prime number must either be adjacent to or a prime distance away from a primorial or primorial product (the distance will be a prime smaller than the candidate). - Bill McEachen, Jun 03 2010
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REFERENCES
| CRC Standard Mathematical Tables, 28th Ed., CRC Press
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Robert Potter, Perfect Numbers.
J. Sokol, Title?
Wikipedia, Primorial
Bill McEachen, Normalized A129912
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FORMULA
| Apart from 1 and 2, numbers of the form 2^k(1)*3^k(2)*5^k(3)*...*p(s)^k(s), where p(s) is s-th prime, k(i)>0 for i=1..s, k(i)-k(i-1) = 0 or 1 for i=2..s and |{k(1),k(2),..,k(s)}|=k(1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 14 2007
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EXAMPLE
| For s = 4 there are 8 (generally 2^(s-1)) such numbers: 210 = 2*3*5*7, 420 = 2^2*3*5*7 = (2*3*5*7)*2, 1260 = 2^2*3^2*5*7 = (2*3*5*7)*(2*3), 6300 = 2^2*3^2*5^2*7 = (2*3*5*7)*(2*3*5), 2520 = 2^3*3^2*5*7 = (2*3*5*7)*(2*3)*2, 12600 = 2^3*3^2*5^2*7 = (2*3*5*7)*(2*3*5)*2, 37800 = 2^3*3^3*5^2*7 = (2*3*5*7)*(2*3*5)*(2*3), 75600 = 2^4*3^3*5^2*7 = (2*3*5*7)*(2*3*5)*(2*3)*2.
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CROSSREFS
| Cf. A002110, A025487.
Sequence in context: A166456 A162214 A100071 * A182863 A161507 A032177
Adjacent sequences: A129909 A129910 A129911 * A129913 A129914 A129915
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KEYWORD
| easy,nonn
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AUTHOR
| Bill McEachen (bmceache(AT)centralsan.dst.ca.us), Jun 05 2007, Jun 06 2007, Jul 06 2007, Aug 07 2007
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 09 2007, Aug 08 2007
I corrected the Potter link to reflect its relocation. - Bill McEachen (bmceache(AT)centralsan.org), Sep 12 2009
I added link to Wikicommons image. - Bill McEachen (bmceache(AT)centralsan.org), Sep 16 2009
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