Sub-perfect Numbers

Joined
Jan 15, 2024
Messages
1
Reaction score
0
Let's call a number N 'sub-perfect' if the sum of its divisors less than N is N-1. (There may be a different term for such numbers). It is easy to see that powers of 2 are sub-perfect. Does anyone know a proof or counter-example to the conjecture that all sub-perfect numbers are powers of 2?
 
The divisors of 9 that are < 9 are 1 and 3. 1+3 = 4, which not= 8. So this is not a counter-example.
 
Last edited:
I think it can be proved by viewing numbers' binary representations.

E.g., 7 = 111 (base 2) = 1+2+4, the divisors of 8 less than 8, which is 7+1.
 
The conjecture that all sub-perfect numbers are powers of 2 is indeed false. A counter-example to this conjecture is 12.

To show that 12 is a sub-perfect number, let's find the sum of its divisors less than 12:

1 + 2 + 3 + 4 + 6 = 16

As the sum of its divisors less than 12 is 16, which is equal to 12 - 1, 12 qualifies as a sub-perfect number.

However, 12 is not a power of 2. Thus, 12 serves as a counter-example to the conjecture.

It is not the easy task to solve such questions. You need to practice it more and solve a lot of assignments to get complete command on it. You can find the samples or get assignment assistance related to it at mathsassignmenthelp.com website. You can also contact them at: +1 (315) 557-6473.
 
Are you trying to get people to call that phone-number, RobertSmart or ROBERTMILLS (or whatever your name is)?
 

Members online

No members online now.

Forum statistics

Threads
2,521
Messages
9,844
Members
700
Latest member
KGWDoris3
Back
Top