Integers n; sum of the reciprocals of prime factors + 1/n = 1

 
 
 
Recip Prime Factors

 

Allowing prime powers among the divisors

k = 7,    n = 144508961850
144508961850 \; = \; 2\cdot 3\cdot 5^2\cdot 11\cdot 29\cdot 1097\cdot 2753
Prime factors :    (2,3,11,25,29,1097,2753)
The sum of the reciprocals (S) is,
1/2 + 1/3 + 1/11 + 1/25 + 1/29 + 1/1097 + 1/2753 = 144508961849/144508961850
(S) + 1/n = 144508961849/144508961850 + 1/144508961850 = 1

 

k = 8,    n = 20882840055109264384350
20882840055109264384350 \; = \; 2\cdot 3\cdot 5^2\cdot 11\cdot 29\cdot 1097\cdot 2753\cdot 144508961851
Prime factors :    (2,3,25,11,29,1097,2753,144508961851)
The sum of the reciprocals (S) is,
1/2 + 1/3 + 1/25 + 1/11 + 1/29 + 1/1097 + 1/2753 + 1/144508961851
= 20882840055109264384349/20882840055109264384350

(S) + 1/n =
= 20882840055109264384349/20882840055109264384350 + 1/20882840055109264384350 = 1

 
 

Is there a solution with 9 prime factors?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s