Find all integers \(n\) such that the arithmetic mean of all its factors is an integer.

Thanks so much!

ibhar Mar 13, 2022

#1**+1 **

Every odd prime number has two factors and only two factors, 1 and the prime number.

The result of adding 1 to the odd prime number is an even number; dividing this

answer by 2 results in an integer.

Now, you have an infinite number of answers.

And yet, there are more; some even numbers also fulfill the requirement ...

geno3141 Mar 14, 2022

#2**+1 **

Oh! That's really cool! I haven't thought of the odd primes.

I also assume that some non-odd primes work and as you say, some even numbers work too. Is there a specific way of describing them or is it just at random?

Thank you so much,geno3141!

ibhar
Mar 14, 2022

#3**+1 **

Thanks Geno,

I think your answer is cool too :)

Attn: ibhar,

Thank you for responsing to Gino's answer so nicely.

BUT

You need to think.

Your statement: "I also assume that some non-odd primes work"

1) Firstly, tell me some non-odd primes.

2) second show me with one of them what the average of its factors is.

3) discuss your answers.

YES you are expected to answer me :)

Melody
Mar 14, 2022