I forgot to do the case for 1
So 1 has 1 factor, that is 1
so the sum of the number of factors squared is 1.
Sum of the cubes of the factors of 1 is 1.
So that is the 1 = 1. The sum of cubes of the factors then becomes larger than the sum of the number of factors of the factors as you go higher one.
Thoughts: Well if I was a high school student, I would be happy with such findings. We were like are we supposed to prove it or?
I figured Stan will have some nice elegant proof.
Woops I read this question over and over again. I think I did this problem wrong the second time. I thought I was doing the sum of the (cubes of the divisors). Eek!
ReplyDeleteWell, technically your conjecture seems to hold true except for the situation of the prime number 1, where you get 1=1. You seemed to have a logical progression, starting with prime numbers and increasing the number of divisors. Looks like everyone in our group came to a different conclusion. Good job two-columning that problem!
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