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A250133
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Denominator of the harmonic mean of the first n composite numbers.
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11
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1, 5, 13, 47, 271, 301, 2287, 491, 1045, 367, 1919, 1999, 22829, 23599, 121691, 1628183, 15054047, 15440147, 15800507, 32276689, 32931889, 570652913, 83022119, 84480719, 1631388461, 1656970061, 1681912121, 11939665247, 12098387447, 12253582487, 285324285601
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OFFSET
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1,2
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COMMENTS
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Also numerator of the sum of the reciprocals of the first n composite numbers (A250133/A296358).
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..500
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EXAMPLE
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a(3) = 13 because the first 3 composite numbers are [4,6,8] and 3 / (1/4+1/6+1/8) = 72/13.
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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PROG
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(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
composite(n) = for(k=0, primepi(n), isprime(n++)&&k--); n \\ from A002808
s=vector(100); for(k=1, #s, s[k]=denominator(harmonicmean(vector(k, i, composite(i))))); s
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CROSSREFS
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Cf. A250132 (numerators).
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: A304964 A120790 A162563 * A025545 A146152 A082132
Adjacent sequences: A250130 A250131 A250132 * A250134 A250135 A250136
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KEYWORD
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nonn
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AUTHOR
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Colin Barker, Nov 14 2014
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STATUS
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approved
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