A250132 Numerator of the harmonic mean of the first n composite numbers.

4, 24, 72, 288, 1800, 2160, 17640, 4032, 9072, 3360, 18480, 20160, 240240, 258720, 1386000, 19219200, 183783600, 194594400, 205405200, 432432000, 454053600, 8086478400, 1207720800, 1260230400, 24942060000, 25939742400, 26937424800, 195545750400, 202529527200

Offset: 1

Author

Colin Barker, Nov 14 2014

Keywords

• nonn

Examples

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

Links

• Colin Barker, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A250133 (denominators).

Programs

Mathematica

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

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