<!DOCTYPE html>
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta charset="utf-8">

<title>Problem 495 - Project Euler</title>
<link rel="shortcut icon" href="favicon.ico">
<link rel="stylesheet" type="text/css" href="pe_template_style.css">

<script type="text/x-mathjax-config">
   MathJax.Hub.Config({
      jax: ["input/TeX", "output/HTML-CSS"],
      tex2jax: {
         inlineMath: [ ["$","$"], ["\\(","\\)"] ],
         displayMath: [ ["$$","$$"], ["\\[","\\]"] ],
         processEscapes: true
      },
      "HTML-CSS": { availableFonts: ["TeX"] }
   });
</script>

<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
</script>
</head>

<body>
<div id="container">

   <div id="nav" class="noprint">
      <ul>
<li><a href="about.html" title="About">About</a></li>
<li id="current"><a href="problems.html" title="Problems">Problems</a></li>
<li><a href="news.html" title="News">News</a></li>
<li><a href="http://forum.projecteuler.net" title="Project Euler Forum">Forum</a></li>
      </ul>
   <div style="text-align:right;padding:30px 10px 0 0;">
      <a href="rss2_euler.xml"><img src="images/icon_rss.png" alt="RSS Feed" title="RSS Feed"></a>
   </div>
   </div>


   <div id="logo" class="noprint">
      <img src="images/pe_banner.png" alt="Project Euler .net">
   </div>

   <div id="content">
<div id="notification">This website is a semi-functional mirror of the original <a href="https://projecteuler.net/">Project Euler</a>. More information is available on <a href="https://github.com/wackyapples/ProjectEulerMirror/blob/gh-pages/README.md">GitHub</a>.</div>
<div style="text-align:center;" class="print"><img src="images/pe_banner.png" alt="projecteuler.net" style="border:none;"></div>
<h2>Writing n as the product of k distinct positive integers</h2>
<h3>Problem 495</h3>
<div style="font-size:80%;color:#999;">Published on 27 December 2014 at 10:00 pm [Server Time]</div>
<div class="problem_content" role="problem">
<p>Let <var>W</var>(<var>n</var>,<var>k</var>) be the number of ways in which <var>n</var> can be written as the product of <var>k</var> distinct positive integers.</p>
<p>For example, <var>W</var>(144,4) = 7. There are 7 ways in which 144 can be written as a product of 4 distinct positive integers:</p>
<p></p>
<ul>
<li>144 = 1×2×4×18</li>
<li>144 = 1×2×8×9</li>
<li>144 = 1×2×3×24</li>
<li>144 = 1×2×6×12</li>
<li>144 = 1×3×4×12</li>
<li>144 = 1×3×6×8</li>
<li>144 = 2×3×4×6</li>
</ul>
<p>Note that permutations of the integers themselves are not considered distinct.</p>
<p>Furthermore, <var>W</var>(100!,10) modulo 1 000 000 007 = 287549200.</p>
<p>Find <var>W</var>(10000!,30) modulo 1 000 000 007.</p>
</div>
<br>
<div style="text-align:center;" class="noprint">Answer not yet available</div>
<div>Go to back to <a href="problems%3Bpage=10.html">Problems</a>
</div>
</div>

   <div id="footer" class="noprint">© Project Euler</div>

<!--/Creative Commons License--><!-- <rdf:RDF xmlns="http://web.resource.org/cc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#">
   <Work rdf:about="">
      <license rdf:resource="http://creativecommons.org/licenses/by-nc-sa/2.0/uk/" />
   <dc:type rdf:resource="http://purl.org/dc/dcmitype/Text" />
   </Work>
   <License rdf:about="http://creativecommons.org/licenses/by-nc-sa/2.0/uk/"><permits rdf:resource="http://web.resource.org/cc/Reproduction"/><permits rdf:resource="http://web.resource.org/cc/Distribution"/><requires rdf:resource="http://web.resource.org/cc/Notice"/><requires rdf:resource="http://web.resource.org/cc/Attribution"/><prohibits rdf:resource="http://web.resource.org/cc/CommercialUse"/><permits rdf:resource="http://web.resource.org/cc/DerivativeWorks"/><requires rdf:resource="http://web.resource.org/cc/ShareAlike"/></License></rdf:RDF> -->
</div>
<div style="height:1px;">                                                                                                                                                                                                                                                                                                            </div>
</body>
</html>