%I #20 Aug 20 2019 09:24:04

%S 4,12,24,72,360,360,2520,504,1008,336,1680,1680,18480,18480,92400,

%T 1201200,10810800,10810800,10810800,21621600,21621600,367567200,

%U 52509600,52509600,997682400,997682400,997682400,6983776800,6983776800,6983776800

%N Denominator of the sum of the reciprocals of the first n composite numbers.

%C Same as A282512 without the initial 1.

%H Amiram Eldar, <a href="/A296358/b296358.txt">Table of n, a(n) for n = 1..3953</a>

%F 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.

%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

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

%Y Numerators are in A250133.

%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,frac

%O 1,1

%A _N. J. A. Sloane_, Dec 15 2017