Integers(a,b,c,d) in A.P. whose number of divisors is also in A.P.

 
 

229,   361,   493,   and   625   are in arithmetic progression:

361   –   229   =   493   –   361   =   625   –   493   =   132

and the number of divisors of each is also in arithmetic progression:

n …….   divisors

229 …..   2     (1   229)
361 …..   3     (1   19   361)
493 …..   4     (1   17   29   493)
625 …..   5     (1   5   25   125   625)

 
 

Can you find another quadruplet of 3-digit numbers?
a quadruplet of 4-digit numbers?
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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