Problem 53029. Easy Sequences 49: Prime Little Omega Function

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>, the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Prime_omega_function\"><w:r><w:t>prime little omega</w:t></w:r></w:hyperlink><w:r><w:t> function, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\omega(n)</w:t></w:r></w:customXml><w:r><w:t>, is defined as the total number of distinct prime factors of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>. So, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=300</w:t></w:r></w:customXml><w:r><w:t>, since </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>300 = 2^2\\cdot3^1\\cdot5^2</w:t></w:r></w:customXml><w:r><w:t>, therefore </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\omega(300) = 3</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, write a function that evaluates the following summation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\sum_{i=1}^{n}(i-\\omega (i))</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n = 10</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\sum_{i=1}^{10}(i-\\omega (i)) = (1-\\omega(1))+(2-\\omega(2))+(3-\\omega(3))+(4-\\omega(4))+(5-\\omega(5))+(6-\\omega(6))+(7-\\omega(7))+(8-\\omega(8))+(9-\\omega(9))+(10-\\omega(10))\\\\ \n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ = (1-0)+(2-1)+(3-1)+(4-1)+(5-1)+(6-2)+(7-1)+(8-1)+(9-1)+(10-2)\\\\ \n\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ = 1+1+2+3+4+4+6+7+8+8 = 44.\n\n</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In this case therefore, the function should return </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>44</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> This is an easier version of the previous problem, '</w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/53009-easy-sequences-48-prime-big-omega-of-factorial-sequence\"><w:r><w:t>Prime Big Omega of Factorial Sequence</w:t></w:r></w:hyperlink><w:r><w:t>'. So, for an added challenge, you may enjoy prime factoring each number, as the MATLAB functions 'factor', 'primes' and 'isprime' will be disabled.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 378px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">For an integer n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, the <a target='_blank' href = "https://en.wikipedia.org/wiki/Prime_omega_function">prime little omega</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> function, <img src="data:image/png;base64,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" width="32.5" height="19" style="width: 32.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, is defined as the total number of distinct prime factors of n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. So, if <img src="data:image/png;base64,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" width="51.5" height="18" style="width: 51.5px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, since <img src="data:image/png;base64,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" width="103.5" height="19" style="width: 103.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, therefore <img src="data:image/png;base64,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" width="73.5" height="19" style="width: 73.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Given an integer n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, write a function that evaluates the following summation:</div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <img src="data:image/png;base64,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" width="84.5" height="46" style="width: 84.5px; height: 46px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">For example for <img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">:</div><div style="block-size: 110px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <img src="data:image/png;base64,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" width="926" height="89" style="width: 926px; height: 89px;"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">In this case therefore, the function should return <img src="data:image/png;base64,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" width="18" height="18" style="width: 18px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">NOTE:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> This is an easier version of the previous problem, '<a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/53009-easy-sequences-48-prime-big-omega-of-factorial-sequence">Prime Big Omega of Factorial Sequence</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">'. So, for an added challenge, you may enjoy prime factoring each number, as the MATLAB functions 'factor', 'primes' and 'isprime' will be disabled.</div></div></div>

Solve

Solution Stats

8 Solutions
4 Solvers

Last Solution submitted on Mar 19, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

William on 13 Nov 2021

Ramon,
In test #7, I think the last digit of the mean(s) is maybe supposed to be a 3 rather than a 5. I'm also having some problems with test #3, but I haven't investigated that yet.

Ramon Villamangca on 14 Nov 2021

Hi William,
I can't see where our difference in test#7 is coming from, because even if I use: mean = int64(sum/numel), I'm still getting 7620740342849265. Could it be because of overflow, again? I tried not to exceed 'flintmax' this time, though. Can you publish your solution, please? Thanks.

Regarding test#3, I've checked my solution using the formula: omega(x) = numel(unique(factor(x))), and it seems correct.

William on 19 Nov 2021

Interesting. My solution fails test #7 on my laptop, but passes on the Cody server. The problem with test #3 was my fault!

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 53029. Easy Sequences 49: Prime Little Omega Function

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author104

Problem Tags

Community Treasure Hunt

Problem 53029. Easy Sequences 49: Prime Little Omega Function

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers4

Suggested Problems

More from this Author104

Problem Tags

Community Treasure Hunt

Players