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<span class="refentrytitle">fareyleni</span>
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<p>fareyleni —
returns the length of a Farey Sequence.
</p>
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<div class="refsect1" title="Description">
<a id="id2845219"></a>
<h2>Description</h2>
<p>
This opcode can be used in conjunction with <a class="link" href="GENfarey.html" title="GENfarey"><em class="citetitle">GENfarey</em></a>.
It calculates the length of Farey Sequence F<sub>n</sub>. Its length is given by:
|F<sub>n</sub>| = 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.
</p>
<p>
Some values for the length of F<sub>n</sub> given n:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" type="disc">
<li class="listitem">n |F<sub>n</sub>|</li>
<li class="listitem">1 2</li>
<li class="listitem">2 3</li>
<li class="listitem">3 5</li>
<li class="listitem">4 7</li>
<li class="listitem">5 11</li>
<li class="listitem">6 13</li>
<li class="listitem">7 19</li>
<li class="listitem">8 23</li>
<li class="listitem">9 29</li>
<li class="listitem">10 33</li>
<li class="listitem">11 43</li>
<li class="listitem">12 47</li>
<li class="listitem">13 59</li>
<li class="listitem">14 65</li>
<li class="listitem">15 73</li>
<li class="listitem">16 81</li>
<li class="listitem">17 97</li>
<li class="listitem">18 103</li>
<li class="listitem">19 121</li>
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<h2>Syntax</h2>
<pre class="synopsis">ifl <span class="command"><strong>fareyleni</strong></span> ifn</pre>
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<div class="refsect1" title="Initialisation">
<a id="id2845829"></a>
<h2>Initialisation</h2>
<p>
The length of the identified Farey sequence is returned.
</p>
<p>
<span class="emphasis"><em>ifn</em></span> -- Integer identifying the sequence.
</p>
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<div class="refsect1" title="Credits">
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<h2>Credits</h2>
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<td>Author: Georg Boenn </td>
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<td>University of Glamorgan, UK</td>
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<p>New in Csound version 5.13</p>
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