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Search: id:A063428
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| A063428 |
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a(n) is the smallest positive integer of the form n*k/(n+k). |
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+0
8
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| 1, 2, 2, 4, 2, 6, 4, 6, 5, 10, 3, 12, 7, 6, 8, 16, 6, 18, 4, 12, 11, 22, 6, 20, 13, 18, 12, 28, 5, 30, 16, 22, 17, 10, 9, 36, 19, 26, 8, 40, 6, 42, 22, 18, 23, 46, 12, 42, 25, 34, 26, 52, 18, 30, 7, 38, 29, 58, 10, 60, 31, 14, 32, 40, 22, 66, 34, 46, 20, 70, 8, 72, 37, 30, 38, 28, 26
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Or, smallest b such that 1/n+1/c=1/b has integer solutions.
Largest b is (n-1) since 1/n+1/(n(n-1))=1/(n-1).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=2,...,1000
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FORMULA
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a(n) = n*A063427(n)/(n+A063427(n)) =2n-A063649(n)
If n is prime a(n)=n-1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 31 2001
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EXAMPLE
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a(6) = 2 because 6*3/(6+3)=2 is the smallest integer of the form 6*k/(6+k).
a(10) = 5 since 1/10+1/10 = 1/5, 1/10+1/15 = 1/6, 1/10+1/40 = 1/8, 1/10+1/90 = 1/9 and so the first sum provides the value.
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PROGRAM
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(PARI) { for (n=2, 1000, k=1; while (n*k%(n + k), k++); write("b063428.txt", n, " ", n*k/(n + k)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 20 2009]
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CROSSREFS
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Cf. A018892, A063427, A127730, A063647, A063648, A063649, A066092.
Sequence in context: A122645 A122646 A028496 this_sequence A133439 A072300 A028913
Adjacent sequences: A063425 A063426 A063427 this_sequence A063429 A063430 A063431
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 19 2001
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EXTENSIONS
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New description from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 31 2001
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Feb 13 2007
Definition revised by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 07 2009
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