20200929, 09:26  #1 
Mar 2018
2^{2}×7×19 Posts 
sigma(n)=x*(x+1)^3
let be sigma(n) the sum of the divisors of n
something is known about numbers n such that sigma(n)=x*(x+1)^3 with x positive integer? for example n=69660, sigma(69660)=21*(22^3) are there infinitely many examples? 
20200929, 10:24  #2 
Romulan Interpreter
"name field"
Jun 2011
Thailand
3^{5}·41 Posts 
wow! you advanced now! this is a step up from the pg(whatever) numbers

20200929, 11:01  #3 
Jun 2003
5×29×37 Posts 

20200929, 12:12  #4 
Feb 2017
Nowhere
169A_{16} Posts 
If x is a positive integer and f(x) = x*(x+1)^3  1 is a prime p, then sigma(p) = p+1 = x*(x+1)^3.
Everyone knows there are infinitely many x for which f(x) is prime (Bunyakovsky and BatemanHorn conjectures), but nobody knows how to prove it. The smallest such x is 1. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
what does sigma mean in ECM?  bbb120  GMPECM  7  20210126 16:18 
Sigma parameter in ecm  storm5510  Information & Answers  4  20191130 21:32 
Iteration of (sigma(n)+phi(n))/2  sean  Factoring  2  20170918 15:39 
Given sigma(n)n, find the smallest possible n  mart_r  Aliquot Sequences  6  20130723 20:50 
Spooky sigma values  lavalamp  Software  2  20100824 15:22 