mersenneforum.org sigma(n)=x*(x+1)^3
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 2020-09-29, 09:26 #1 enzocreti   Mar 2018 21416 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?
 2020-09-29, 10:24 #2 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 25×313 Posts wow! you advanced now! this is a step up from the pg(whatever) numbers
2020-09-29, 11:01   #3
axn

Jun 2003

22·3·449 Posts

Quote:
 Originally Posted by LaurV wow! you advanced now! this is a step up from the pg(whatever) numbers
69660 is a pg prime thingie. Sorry to disappoint you.

 2020-09-29, 12:12 #4 Dr Sardonicus     Feb 2017 Nowhere 171B16 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 Bateman-Horn conjectures), but nobody knows how to prove it. The smallest such x is 1.

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