fareylen
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## fareylen

fareylen — returns the length of a Farey Sequence.

## Description

This opcode can be used in conjunction with GENfarey. It calculates the length of Farey Sequence Fn. Its length is given by: |Fn| = 1 + SUM over n phi(m) where phi(m) is Euler's totient function, which gives the number of integers ≤ m that are coprime to m.

Some values for the length of Fn given n:

n | Fn
--- | ---
1 | 2
2 | 3
3 | 5
4 | 7
5 | 11
6 | 13
7 | 19
8 | 23
9 | 29
10 | 33
11 | 43
12 | 47
13 | 59
14 | 65
15 | 73
16 | 81
17 | 97
18 | 103
19 | 121
20 | 129

## Syntax

    kfl fareylen kfn

## Performance

The length of the identified Farey sequence is returned.

kfn -- Integer identifying the sequence.

## Credits

Author: Georg Boenn
University of Glamorgan, UK

New in Csound version 5.13

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