My Math Forum Summation of all proper divisor

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 May 14th, 2014, 06:04 AM #1 Member   Joined: Apr 2014 From: Missouri Posts: 39 Thanks: 1 Summation of all proper divisor What is the maximum 4 digit integer n for which the sum of its proper divisors is (n-1)? Thanks in advance
 May 14th, 2014, 07:12 AM #2 Senior Member   Joined: Nov 2010 Posts: 288 Thanks: 1 u may notice that for the sum of divisors of an integer n to be n-1 it should be of the form 2^k to find the maximum integer u have to find k to do that u may solve the following: 2^k=9999(where 9999 is the maximum four digit integer) then k=ln9999/ln2 =13.2..... then k=13 and hence n=2^13=8192
 May 14th, 2014, 07:27 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2643 Math Focus: Mainly analysis and algebra Oops! I used the wrong definition of proper divisors! Last edited by v8archie; May 14th, 2014 at 07:32 AM.
 May 14th, 2014, 07:42 AM #4 Member   Joined: Apr 2014 From: Missouri Posts: 39 Thanks: 1 Hi Islam Thanks for your answer. But How did you get this formula like: If the sum of all proper divisor of n to be (n-1) then n=2^k? Why did we take ln? Why cant we take log? Thanks in advance and Regards
 May 14th, 2014, 07:45 AM #5 Member   Joined: Apr 2014 From: Missouri Posts: 39 Thanks: 1 Hi Islam It gives you the same result using ln and log. So one question is solved. But what is the formula for this? Thanks
 May 14th, 2014, 08:48 AM #6 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra

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### maximum proper divisor equation

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