Problem 45424. Amicable pair

Created by Asif Newaz

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Amicable numbers are two different numbers such that the sum of the proper divisors of each is equal to the other number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 220 = 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110  ; sum =284\n 284 = 1, 2, 4, 71, 142  ; sum =220]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So, 220 &amp; 284 make an amicable pair.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Find the number of such pairs within n.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://oeis.org/A259180\"><w:r><w:t>&lt;https://oeis.org/A259180</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

10 Solutions
6 Solvers

Last Solution submitted on Dec 01, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Rafael S.T. Vieira on 6 Sep 2020

The 8th test case is correct and can be solved within Cody's time limit. Why is it not being used? Up to 200.000, there are 20 amicable pairs.

Rafael S.T. Vieira on 6 Sep 2020

For instance 176272,180848 is the 20th pair. For 3e5 my code can't go fast enough for Cody (45s), but I've found just 2 additional pairs 196724, 202444 and 185368, 203432.

Problem Recent Solvers6

Problem Tags

number theory

Community Treasure Hunt

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

Start Hunting!

Problem 45424. Amicable pair

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author149

Problem Tags

Community Treasure Hunt

Problem 45424. Amicable pair

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author149

Problem Tags

Community Treasure Hunt

Players