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	<id>https://number.subwiki.org/w/index.php?action=history&amp;feed=atom&amp;title=Square-free_kernel</id>
	<title>Square-free kernel - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://number.subwiki.org/w/index.php?action=history&amp;feed=atom&amp;title=Square-free_kernel"/>
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	<updated>2026-09-04T08:11:31Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.41.2</generator>
	<entry>
		<id>https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=221&amp;oldid=prev</id>
		<title>Vipul at 02:34, 29 April 2009</title>
		<link rel="alternate" type="text/html" href="https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=221&amp;oldid=prev"/>
		<updated>2009-04-29T02:34:12Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 02:34, 29 April 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Definition==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Definition==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; be a [[natural number]]. The &#039;&#039;&#039;square-free part&#039;&#039;&#039; of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; is the product of all the prime divisors of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; be a [[natural number]]. The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;square-free kernel&#039;&#039;&#039; or &lt;/ins&gt;&#039;&#039;&#039;square-free part&#039;&#039;&#039; of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; is the product of all the prime divisors of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Relation with other arithmetic functions==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Relation with other arithmetic functions==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
	<entry>
		<id>https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=219&amp;oldid=prev</id>
		<title>Vipul: moved Square-free part to Square-free kernel</title>
		<link rel="alternate" type="text/html" href="https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=219&amp;oldid=prev"/>
		<updated>2009-04-29T02:33:45Z</updated>

		<summary type="html">&lt;p&gt;moved &lt;a href=&quot;/wiki/Square-free_part&quot; class=&quot;mw-redirect&quot; title=&quot;Square-free part&quot;&gt;Square-free part&lt;/a&gt; to &lt;a href=&quot;/wiki/Square-free_kernel&quot; title=&quot;Square-free kernel&quot;&gt;Square-free kernel&lt;/a&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 02:33, 29 April 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;en&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
	<entry>
		<id>https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=215&amp;oldid=prev</id>
		<title>Vipul: Created page with &#039;{{arithmetic function}}  ==Definition==  Let &lt;math&gt;n&lt;/math&gt; be a natural number. The &#039;&#039;&#039;square-free part&#039;&#039;&#039; of &lt;math&gt;n&lt;/math&gt; is the product of all the prime divisors of &lt;mat...&#039;</title>
		<link rel="alternate" type="text/html" href="https://number.subwiki.org/w/index.php?title=Square-free_kernel&amp;diff=215&amp;oldid=prev"/>
		<updated>2009-04-29T02:12:47Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;#039;{{arithmetic function}}  ==Definition==  Let &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; be a &lt;a href=&quot;/w/index.php?title=Natural_number&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Natural number (page does not exist)&quot;&gt;natural number&lt;/a&gt;. The &amp;#039;&amp;#039;&amp;#039;square-free part&amp;#039;&amp;#039;&amp;#039; of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; is the product of all the prime divisors of &amp;lt;mat...&amp;#039;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{arithmetic function}}&lt;br /&gt;
&lt;br /&gt;
==Definition==&lt;br /&gt;
&lt;br /&gt;
Let &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; be a [[natural number]]. The &amp;#039;&amp;#039;&amp;#039;square-free part&amp;#039;&amp;#039;&amp;#039; of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; is the product of all the prime divisors of &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
==Relation with other arithmetic functions==&lt;br /&gt;
&lt;br /&gt;
* [[Prime divisor count function]]&lt;br /&gt;
&lt;br /&gt;
==Properties==&lt;br /&gt;
&lt;br /&gt;
{{multiplicative}}&lt;br /&gt;
&lt;br /&gt;
{{divisibility-preserving}}&lt;/div&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
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