20200929, 09:26  #1 
Mar 2018
1017_{8} 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
Jun 2011
Thailand
9168_{10} Posts 
wow! you advanced now! this is a step up from the pg(whatever) numbers

20200929, 11:01  #3 
Jun 2003
2×5^{2}×97 Posts 

20200929, 12:12  #4 
Feb 2017
Nowhere
2^{2}×1,049 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. 
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