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A051451
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LCM{ 1,2,...,x } where x is a prime power (A000961).
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45
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1, 2, 6, 12, 60, 420, 840, 2520, 27720, 360360, 720720, 12252240, 232792560, 5354228880, 26771144400, 80313433200, 2329089562800, 72201776446800, 144403552893600, 5342931457063200, 219060189739591200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This may be the "smallest" product-based numbering system that has a unique finite representation for every rational number. In this base 1/2 = .1 (1*1/2), 1/3 = .02 (0*1/2 + 2*1/6), 1/5 = .0102 (0*1/2 + 1*1/6 + 0*1/12 + 2*1/60). - Russell Easterly (logiclab(AT)attbi.com), Oct 03 2001
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
R. Easterly, Product Based Numbering Systems
Index entries for sequences related to lcm's
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FORMULA
| a(n) = A003418(A000961(n)).
Distinct values of A003418, i.e. A051451 = Union[A003418].
Partial products of A025473, prime roots of the prime powers.
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EXAMPLE
| LCM[1,..,n] is 2520 for n=9 and 10. The smallest such n's are always prime powers, where A003418 jumps.
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MATHEMATICA
| f[n_] := LCM @@ Range@ n; Union@ Array[f, 41] (* Robert G. Wilson v, July 11 2011 *)
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CROSSREFS
| Cf. A000961, A003418, A025473, A049536, A049537.
Sequence in context: A048803 A068625 A162935 * A090951 A168262 A085819
Adjacent sequences: A051448 A051449 A051450 * A051452 A051453 A051454
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| Minor edits by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jan 16 2009
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