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Search: id:A025529
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| A025529 |
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a(n) = (1/1 + 1/2 + ... + 1/n)*LCM{1,2,...,n}. |
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+0
8
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| 1, 3, 11, 25, 137, 147, 1089, 2283, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 42822903, 825887397, 837527025, 848612385, 859193865, 19994251455, 20217344325, 102157567401, 103187226801, 312536252003
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Bernoulli numbers and Leibniz's harmonic triangle (see A003506): Akiyama-Tanigawa algorithm from (a(n)/A058312)=1,3/2,11/6,25/12,137/60,147/60,1089/420,2283/840,7129/2520, leads to Bernoulli numbers A027641/A027642. To prove. Second row: -1/2,-2/3,-3/4,=-A000027/A020725. First fractions are companions to (A000012/A000027)=1,1/2,1/3,1/4,1/5, (like A027641 and A164555). Link: 2,4,12,24,120,120,=A051426=2*A058312. [From Paul Curtz (bpcrtz(AT)free.fr), Feb 06 2010]
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CROSSREFS
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Sequence in context: A111935 A001008 A096617 this_sequence A124078 A096795 A160039
Adjacent sequences: A025526 A025527 A025528 this_sequence A025530 A025531 A025532
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KEYWORD
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nonn,new
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Removed the formulas involving sums of binomials.. they are wrong. sum{k=0..n, sum{j=0..k, binomial(k, j)(-1)^j/(j+1) }} != (1/1 + 1/2 + ... + 1/n) with any offset Stephen Crowley (crow(AT)crowlogic.net), Jul 11 2009
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