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Search: id:A120369
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| A120369 |
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Smallest value of k where n*k^(1/n) >= (n+1)*k^(1/(n+1)). |
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+0
1
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| 4, 12, 32, 87, 238, 649, 1769, 4820, 13128, 35744, 97295, 264783, 720465, 1960095, 5332044, 14503451, 39447240, 107283957, 291762849, 793424505, 2157567407, 5866897880, 15952911029, 43377066302, 117942558396, 320680213521
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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To minimize the sum of the parts whose product is k, all k, a(n) <= k < a(n+1) should be split into n parts.
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FORMULA
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a(n) = ceiling[((n+1)/n)^((n+1)*n)]
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EXAMPLE
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a(2) = 12 because 2*sqrt(11) is less than 3*cuberoot(11), but 2*sqrt(12) is more than 3*cuberoot(12). a(3) = 32 because 3*cuberoot(31) is less than 4*fourthroot(31), but the inequality reverses at 32.
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CROSSREFS
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Sequence in context: A038592 A048776 A135248 this_sequence A001665 A066536 A104747
Adjacent sequences: A120366 A120367 A120368 this_sequence A120370 A120371 A120372
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KEYWORD
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easy,nonn
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AUTHOR
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Joshua Zucker and Julian Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 27 2006
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