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A250133 Denominator of the harmonic mean of the first n composite numbers. 11

%I

%S 1,5,13,47,271,301,2287,491,1045,367,1919,1999,22829,23599,121691,

%T 1628183,15054047,15440147,15800507,32276689,32931889,570652913,

%U 83022119,84480719,1631388461,1656970061,1681912121,11939665247,12098387447,12253582487,285324285601

%N Denominator of the harmonic mean of the first n composite numbers.

%C Also numerator of the sum of the reciprocals of the first n composite numbers (A250133/A296358).

%H Colin Barker, <a href="/A250133/b250133.txt">Table of n, a(n) for n = 1..500</a>

%e a(3) = 13 because the first 3 composite numbers are [4,6,8] and 3 / (1/4+1/6+1/8) = 72/13.

%e 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

%o (PARI)

%o harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])

%o composite(n) = for(k=0, primepi(n), isprime(n++)&&k--); n \\ from A002808

%o s=vector(100); for(k=1, #s, s[k]=denominator(harmonicmean(vector(k, i, composite(i))))); s

%Y Cf. A250132 (numerators).

%Y 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.

%K nonn

%O 1,2

%A _Colin Barker_, Nov 14 2014

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)