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Search: id:A051451
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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
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OFFSET
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1,2
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COMMENT
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Product of the prime roots of the prime powers.
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
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T. D. Noe, Table of n, a(n) for n=1..100
Index entries for sequences related to lcm's
R. Easterly, Product Based Numbering Systems
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FORMULA
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a(n) = a(n-1)*rootp(n) where rootp is the least prime root of the n-th prime power.
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EXAMPLE
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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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CROSSREFS
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A003418[A[000961(n)]], corresponds to distinct values of A003418. Cf. A049536, A049537.
Product of first n+1 terms of A025473. Cf. A000961.
Sequence in context: A072938 A048803 A068625 this_sequence A090951 A085819 A069047
Adjacent sequences: A051448 A051449 A051450 this_sequence A051452 A051453 A051454
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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