A296358 Denominator of the sum of the reciprocals of the first n composite numbers.

4, 12, 24, 72, 360, 360, 2520, 504, 1008, 336, 1680, 1680, 18480, 18480, 92400, 1201200, 10810800, 10810800, 10810800, 21621600, 21621600, 367567200, 52509600, 52509600, 997682400, 997682400, 997682400, 6983776800, 6983776800, 6983776800

Offset: 1

Author

N. J. A. Sloane, Dec 15 2017

Keywords

• nonn
• frac

Comments

Same as A282512 without the initial 1.

Examples

			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

• Amiram Eldar, Table of n, a(n) for n = 1..3953

Crossrefs

Numerators are in A250133.

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

Mathematica

Accumulate[1/Select[Range[100],CompositeQ]]//Denominator (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 19 2018 *)

Formula

Gerry Felderman (Personal communication, Dec 15 2017) observes that Sum_{k=1..n} 1/composite(k) (= A250133(n)/A296358(n)) ~ log(n) - loglog(n) ~ log pi(n) as n -> oo.