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

1,1

Comments

Same as A282512 without the initial 1.

Links

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

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.

Example

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

Mathematica

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

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.

Sequence in context: A216244 A215223 A318610 * A282512 A025543 A064354

Adjacent sequences: A296355 A296356 A296357 * A296359 A296360 A296361

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 15 2017

Status

approved