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A296358
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Denominator of the sum of the reciprocals of the first n composite numbers.
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10
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4, 12, 24, 72, 360, 360, 2520, 504, 1008, 336, 1680, 1680, 18480, 18480, 92400, 1201200, 10810800, 10810800, 10810800, 21621600, 21621600, 367567200, 52509600, 52509600, 997682400, 997682400, 997682400, 6983776800, 6983776800, 6983776800
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OFFSET
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1,1
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COMMENTS
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Same as A282512 without the initial 1.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..3953
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FORMULA
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Gerry Felderman (Personal communication, Dec 15 2017) observes that Sum_{k=1..n} 1/composite(k) (= A250133(n)/A296358(n)) ~ log(n) - loglog(n) ~ log pi(n) as n -> oo.
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EXAMPLE
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1/4, 5/12, 13/24, 47/72, 271/360, 301/360, 2287/2520, 491/504, 1045/1008, 367/336, 1919/1680, 1999/1680, 22829/18480, ... = A250133/A296358
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MATHEMATICA
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Accumulate[1/Select[Range[100], CompositeQ]]//Denominator (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 19 2018 *)
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CROSSREFS
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Numerators are in A250133.
The following fractions are all related to each other: Sum 1/n: A001008/A002805, Sum 1/prime(n): A024451/A002110 and A106830/A034386, Sum 1/nonprime(n): A282511/A282512, Sum 1/composite(n): A250133/A296358.
Sequence in context: A216244 A215223 A318610 * A282512 A025543 A064354
Adjacent sequences: A296355 A296356 A296357 * A296359 A296360 A296361
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane, Dec 15 2017
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STATUS
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approved
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