cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A296358 #20 Aug 20 2019 09:24:04
%S A296358 4,12,24,72,360,360,2520,504,1008,336,1680,1680,18480,18480,92400,
%T A296358 1201200,10810800,10810800,10810800,21621600,21621600,367567200,
%U A296358 52509600,52509600,997682400,997682400,997682400,6983776800,6983776800,6983776800
%N A296358 Denominator of the sum of the reciprocals of the first n composite numbers.
%C A296358 Same as A282512 without the initial 1.
%H A296358 Amiram Eldar, <a href="/A296358/b296358.txt">Table of n, a(n) for n = 1..3953</a>
%F A296358 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 A296358 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 A296358 Accumulate[1/Select[Range[100],CompositeQ]]//Denominator (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 19 2018 *)
%Y A296358 Numerators are in A250133.
%Y A296358 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 A296358 nonn,frac
%O A296358 1,1
%A A296358 _N. J. A. Sloane_, Dec 15 2017