The definition: we define number as semi perfect , if the number equals to the sum of exactly k of its divisors.
the question: prove that for every n (n>0 | n belong to N) n is semi perfect order 3 if and only if n is divided by 6.
my attempt:
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n is divided by 6 because of that, its divisors are $$\frac{n}{6} ,\frac{n}{2} ,\frac{n}{3} $$
we will sum those 3 divisors - $$\frac{n}{6} + \frac{n}{2} + \frac{n}{3} = n$$ and we finished the proof for one side
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this is the side I have a bit more problem with I know n uphold the definition above but Im having trouble proving that n is divided by 6 with no remainder.
I thought maybe trying with contradiction ( assuming it doesnt divided by 6) but still stuck with this question
would love to please have some help with it