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<h2>
<span class="refentrytitle">fareylen</span>
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<p>fareylen —
returns the length of a Farey Sequence.
</p>
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<div class="refsect1" title="Description">
<a id="idp19810760"></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>
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<colgroup>
<col />
<col />
</colgroup>
<thead>
<tr>
<th>n</th>
<th>F<sub>n</sub></th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>3</td>
<td>5</td>
</tr>
<tr>
<td>4</td>
<td>7</td>
</tr>
<tr>
<td>5</td>
<td>11</td>
</tr>
<tr>
<td>6</td>
<td>13</td>
</tr>
<tr>
<td>7</td>
<td>19</td>
</tr>
<tr>
<td>8</td>
<td>23</td>
</tr>
<tr>
<td>9</td>
<td>29</td>
</tr>
<tr>
<td>10</td>
<td>33</td>
</tr>
<tr>
<td>11</td>
<td>43</td>
</tr>
<tr>
<td>12</td>
<td>47</td>
</tr>
<tr>
<td>13</td>
<td>59</td>
</tr>
<tr>
<td>14</td>
<td>65</td>
</tr>
<tr>
<td>15</td>
<td>73</td>
</tr>
<tr>
<td>16</td>
<td>81</td>
</tr>
<tr>
<td>17</td>
<td>97</td>
</tr>
<tr>
<td>18</td>
<td>103</td>
</tr>
<tr>
<td>19</td>
<td>121</td>
</tr>
<tr>
<td>20</td>
<td>129</td>
</tr>
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</p>
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<div class="refsect1" title="Syntax">
<a id="idp19876648"></a>
<h2>Syntax</h2>
<pre class="synopsis">kfl <span class="command"><strong>fareylen</strong></span> kfn</pre>
</div>
<div class="refsect1" title="Performance">
<a id="idp19877744"></a>
<h2>Performance</h2>
<p>
The length of the identified Farey sequence is returned.
</p>
<p>
<span class="emphasis"><em>kfn</em></span> -- Integer identifying the sequence.
</p>
</div>
<div class="refsect1" title="Credits">
<a id="idp19878992"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
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<td>Author: Georg Boenn </td>
</tr>
<tr>
<td>University of Glamorgan, UK</td>
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<p>New in Csound version 5.13</p>
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