PAT/source/html/b1087.html

有多少不同的值
<div class="ques-view"><p>当自然数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>n</mi></mrow>n</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span> 依次取 1、2、3、……、<span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> 时，算式 <span class="katex"><span class="katex-mathml"><math><mrow><mo>⌊</mo><mi>n</mi><mi mathvariant="normal">/</mi><mn>2</mn><mo>⌋</mo><mo>+</mo><mo>⌊</mo><mi>n</mi><mi mathvariant="normal">/</mi><mn>3</mn><mo>⌋</mo><mo>+</mo><mo>⌊</mo><mi>n</mi><mi mathvariant="normal">/</mi><mn>5</mn><mo>⌋</mo></mrow>\lfloor n/2\rfloor +\lfloor n/3\rfloor +\lfloor n/5\rfloor </math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mopen">⌊</span><span class="mord mathit">n</span><span class="mord mathrm">/</span><span class="mord mathrm">2</span><span class="mclose">⌋</span><span class="mbin">+</span><span class="mopen">⌊</span><span class="mord mathit">n</span><span class="mord mathrm">/</span><span class="mord mathrm">3</span><span class="mclose">⌋</span><span class="mbin">+</span><span class="mopen">⌊</span><span class="mord mathit">n</span><span class="mord mathrm">/</span><span class="mord mathrm">5</span><span class="mclose">⌋</span></span></span></span> 有多少个不同的值？（注：<span class="katex"><span class="katex-mathml"><math><mrow><mo>⌊</mo><mi>x</mi><mo>⌋</mo></mrow>\lfloor x\rfloor</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mopen">⌊</span><span class="mord mathit">x</span><span class="mclose">⌋</span></span></span></span> 为取整函数，表示不超过 <span class="katex"><span class="katex-mathml"><math><mrow><mi>x</mi></mrow>x</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">x</span></span></span></span> 的最大自然数，即 <span class="katex"><span class="katex-mathml"><math><mrow><mi>x</mi></mrow>x</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">x</span></span></span></span> 的整数部分。）</p>
<h3 id="-">输入格式：</h3>
<p>输入给出一个正整数 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>（<span class="katex"><span class="katex-mathml"><math><mrow><mn>2</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>1</mn><msup><mn>0</mn><mn>4</mn></msup></mrow>2 \le N \le 10^4</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.950078em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">2</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">4</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span>）。</p>
<h3 id="-">输出格式：</h3>
<p>在一行中输出题面中算式取到的不同值的个数。</p>
<h3 id="-">输入样例：</h3>
<pre><code class="lang-in">2017
</code></pre>
<h3 id="-">输出样例：</h3>
<pre><code class="lang-out">1480
</code></pre>
</div>