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Numerator of the harmonic mean of the first n composite numbers.
2

%I #10 Jun 30 2017 11:32:27

%S 4,24,72,288,1800,2160,17640,4032,9072,3360,18480,20160,240240,258720,

%T 1386000,19219200,183783600,194594400,205405200,432432000,454053600,

%U 8086478400,1207720800,1260230400,24942060000,25939742400,26937424800,195545750400,202529527200

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

%H Colin Barker, <a href="/A250132/b250132.txt">Table of n, a(n) for n = 1..500</a>

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

%t Module[{comps=Select[Range[50],CompositeQ],len},len=Length[comps];Table[ HarmonicMean[ Take[comps,n]],{n,len}]]//Numerator (* _Harvey P. Dale_, Jun 30 2017 *)

%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]=numerator(harmonicmean(vector(k, i, composite(i))))); s

%Y Cf. A250133 (denominators).

%K nonn

%O 1,1

%A _Colin Barker_, Nov 14 2014