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<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for lcm_sum.cpp:</div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a04065193d190d605e1f0d0d93a87e244" id="r_a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a> (const uint16_t &amp;num)</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\). </p>
<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) where \(\mathrm{LCM}(i,n)\) denotes the Least Common Multiple of the integers i and n. For n greater than or equal to 1. The value of the sum is calculated by formula: </p><p class="formulaDsp">
\[ \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d *
\mathrm{ETF}(d)) + 1\right) * n\right] \]
</p>
<p> where \mathrm{ETF}(i) represents Euler totient function of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/chestamittal" target="_blank">Chesta Mittal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 97</span> {</div>
<div class="line"><span class="lineno"> 98</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 100</span>}</div>
<div class="ttc" id="alcm__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> lcm_sum.cpp:66</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<p>Function for testing lcmSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
<div class="line"><span class="lineno"> 67</span> uint64_t n = 2;</div>
<div class="line"><span class="lineno"> 68</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> == 4);</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> n = 5;</div>
<div class="line"><span class="lineno"> 73</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> == 55);</div>
<div class="line"><span class="lineno"> 75</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 2!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> n = 10;</div>
<div class="line"><span class="lineno"> 78</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 79</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> == 320);</div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> n = 11;</div>
<div class="line"><span class="lineno"> 83</span> uint64_t test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 84</span> assert(test_4 == 616);</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> n = 15;</div>
<div class="line"><span class="lineno"> 88</span> uint64_t test_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 89</span> assert(test_5 == 1110);</div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 5!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 91</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="aheavy__light__decomposition_8cpp_html_a34b8683a2b429de5cce57e6d733ec817"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a></div><div class="ttdeci">static void test_1()</div><div class="ttdef"><b>Definition</b> heavy_light_decomposition.cpp:505</div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_a458410412185a5f09199deaff7157a8d"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a></div><div class="ttdeci">static void test_2()</div><div class="ttdef"><b>Definition</b> heavy_light_decomposition.cpp:549</div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_af31ec5409537703d9c8a47350386b32a"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a></div><div class="ttdeci">static void test_3()</div><div class="ttdef"><b>Definition</b> heavy_light_decomposition.cpp:592</div></div>
<div class="ttc" id="anamespacemath_html_a04065193d190d605e1f0d0d93a87e244"><div class="ttname"><a href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a></div><div class="ttdeci">uint64_t lcmSum(const uint16_t &amp;num)</div><div class="ttdef"><b>Definition</b> lcm_sum.cpp:30</div></div>
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