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? 
wow! you advanced now! this is a step up from the pg(whatever) numbers :lol:

[QUOTE=LaurV;558210]wow! you advanced now! this is a step up from the pg(whatever) numbers :lol:[/QUOTE]
69660 is a pg prime thingie. Sorry to disappoint you. 
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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