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

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

Offset: 1

Author

Colin Barker, Nov 14 2014

Keywords

• nonn

Comments

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

Examples

			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
		

Links

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

Crossrefs

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.

Programs

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