My Math Forum Numbers x such that the sum of the divisors is a perfect square.
 User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 May 7th, 2016, 06:50 AM #1 Newbie   Joined: May 2014 From: India Posts: 7 Thanks: 0 Numbers x such that the sum of the divisors is a perfect square. Hello I am reading "The Theory of Numbers, by Robert D. Carmichael" and stuck in an exercise problem, Find numbers x such that the sum of the divisors of x is a perfect square. I know sum of divisors of a x=$\displaystyle x=p_1^{{\alpha}_1}.p_2^{{\alpha}_2}...p_n^{{\alpha }_i}$ is Sum of divisors =$\displaystyle =\prod{\frac{p_i^{{\alpha}_i+1}-1}{p_i-1}}$ But couldn't proceed further on how resolve the product in to X2 It will be helpful if someone supply some hints
 May 7th, 2016, 08:42 PM #2 Senior Member   Joined: Feb 2012 Posts: 144 Thanks: 16 I think you are counting 1 several times.
 May 8th, 2016, 08:11 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond 1, 3, 15, 105, 945 ... depending on how you factor them and using only proper divisors.
 May 9th, 2016, 04:40 AM #4 Global Moderator   Joined: Dec 2006 Posts: 19,992 Thanks: 1855 Also 12, as 1 + 2 + 3 + 4 + 6 = 16 = 4². However, the problem states "divisors", not "proper divisors". As the problem doesn't ask for all numbers, it would suffice to provide 1, 3 and 22 (see here).
 May 9th, 2016, 01:43 PM #5 Newbie   Joined: May 2014 From: India Posts: 7 Thanks: 0 Thanks everyone; I have seen the OEIS series, skipjack. I was wondering whether there is any general form for such numbers, as OEIS doesn't seem to mention it. Last edited by skipjack; December 13th, 2016 at 11:53 PM.

 Tags divisors, numbers, perfect, square, sum, umbers

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post greg1313 Number Theory 5 November 28th, 2011 07:16 AM PRO Number Theory 6 August 3rd, 2011 06:38 PM calligraphy Number Theory 4 February 10th, 2011 06:34 AM Barbarel Number Theory 2 November 7th, 2009 02:28 PM momo Number Theory 2 September 18th, 2008 01:58 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2018 My Math Forum. All rights reserved.