Factor Average

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What are the last 3 digits of the average of all the factors 100000 100000 ? The average is rounded off to the nearest integer.


The answer is 836.

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1 solution

Bogdan Simeonov
Dec 31, 2013

We just need to find what's the value of

σ ( n ) τ ( n ) \frac{\sigma(n)}{\tau(n)} for n=10 000.We use the formulas τ ( n ) = p n υ p ( n ) \tau(n)=\displaystyle\prod_{p|n}\upsilon_p(n) and σ ( n ) = p n p υ p ( n ) + 1 1 p 1 \sigma(n)= \displaystyle\prod_{p|n} \frac{p^{\upsilon_p(n)+1}-1}{p-1} .

After calculating, we get the answer 836 \boxed{836}

For the τ ( n ) \tau(n) formula you have to add 1 to the υ p ( n ) \upsilon_p(n)

Bogdan Simeonov - 7 years, 5 months ago

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