Problem 45424. Amicable pair

Created by Asif Newaz

Solve Later

Amicable numbers are two different numbers such that the sum of the proper divisors of each is equal to the other number.
For example,
 220 = 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110  ; sum =284
 284 = 1, 2, 4, 71, 142  ; sum =220
So, 220 & 284 make an amicable pair.
Find the number of such pairs within n.
<https://oeis.org/A259180>
Update - Test cases added at 09-09-22

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20 Solutions
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Last Solution submitted on Jun 19, 2025

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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.

Dyuman Joshi on 9 Sep 2022

Test cases added (upper limit changed from 5e4 to 7.5e4).
More test cases might be added later (upper limit 9e4)

Note - Some solutions have failed to run in cody time limit for test case 7.5e4, and some more will fail for 9e4.

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Problem 45424. Amicable pair

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Problem 45424. Amicable pair

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Last 200 Solutions

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Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author174

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