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Search: id:A057793
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| A057793 |
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Integer nearest Riemann(10^n), where Riemann(x) = Sum of ( mu(k)/k * Integral Log( x^(1/k) ) for k = 1 to infinity. |
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+0
3
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| 5, 26, 168, 1227, 9587, 78527, 664667, 5761552, 50847455, 455050683, 4118052495, 37607910542, 346065531066, 3204941731602, 29844570495887, 279238341360977, 2623557157055978, 24739954284239494, 234057667300228940
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Riemann(x) is Riemann's approximation for the number of primes less than x.
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REFERENCES
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John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144-146.
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LINKS
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Eric Weisstein's World of Mathematics, Riemann Prime Number Formula
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MATHEMATICA
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Rie[n_Integer] := Sum[N[LogIntegral[n^(1/k)]*MoebiusMu[k]/k, 36], {k, 1, 100}]; Table[Round[Rie[10^n]], {n, 1, 21}]
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CROSSREFS
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Adjacent sequences: A057790 A057791 A057792 this_sequence A057794 A057795 A057796
Sequence in context: A082029 A001705 A081047 this_sequence A090226 A094422 A121750
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2000
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EXTENSIONS
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a(1) corrected by Chris Katscher (spatch3(AT)yahoo.com), May 25, 2003
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