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<div id="projectname">Algorithms_in_C++
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 <span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="title">math Namespace Reference</div> </div>
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<div class="contents">
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a>
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<a href="../../dd/d47/namespacemath.html#details">More...</a></p>
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<table class="memberdecls">
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Functions</h2></td></tr>
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<tr class="memitem:a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">lcmSum</a> (const uint16_t &num)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a> </p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for assert</p>
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<p>Mathematical algorithms </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a04065193d190d605e1f0d0d93a87e244"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a04065193d190d605e1f0d0d93a87e244">◆ </a></span>lcmSum()</h2>
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<td class="memname">uint64_t math::lcmSum </td>
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<td>(</td>
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<td class="paramtype">const uint16_t & </td>
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<td class="paramname"><em>num</em></td><td>)</td>
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<td></td>
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<p>Function to compute sum of euler totients in sumOfEulerTotient vector </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">num</td><td>input number </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num </dd></dl>
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<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  {</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  uint64_t i=0, j=0;</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector <uint64_t></a> eulerTotient(num+1);</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector <uint64_t></a> sumOfEulerTotient(num+1);</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  </div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">// storing initial values in eulerTotient vector</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">for</span>(i=1; i<=num; i++) {</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  eulerTotient[i] = i;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  }</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  </div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">// applying totient sieve </span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span>(i=2; i<=num; i++) {</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">if</span>(eulerTotient[i] == i) {</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">for</span>(j=i; j<=num; j+=i) {</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  eulerTotient[j] = eulerTotient[j]/i;</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  eulerTotient[j] = eulerTotient[j]*(i-1);</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  }</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  }</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  }</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  </div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// computing sum of euler totients</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">for</span>(i=1; i<=num; i++) {</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">for</span>(j=i; j <=num; j+=i) {</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  sumOfEulerTotient[j] += eulerTotient[i]*i;</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  }</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">return</span> ((sumOfEulerTotient[num] + 1 ) * num) / 2;</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
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