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-   -   sigma(n)=x*(x+1)^3 (https://www.mersenneforum.org/showthread.php?t=26017)

enzocreti 2020-09-29 09:26

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?

LaurV 2020-09-29 10:24

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

axn 2020-09-29 11:01

[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.

Dr Sardonicus 2020-09-29 12:12

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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