Problem 52769. Easy Sequences 22: Sum of Proper Fractions

Ramon Villamangca

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Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:
            
Note that '2/4' and '3/9' are not included because they are not in their lowest term, while '7/7' and '8/5' are not included because they are not proper fractions.
Write a function 'S(d)', which is the integer part of the sum of 'F(d)'.  For the case above, the sum of elements of 'F(10)' is exactly '15.5'. Therefore S(10) = 15.

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Last Solution submitted on May 24, 2026

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David Hill on 23 Sep 2021

Could not figure out how to speed up my code. Ended up having to use a lookup table to speed it up sufficiently.

Ramon Villamangca on 28 Sep 2021

Hi,

There is a shortcut using Mobius Inversion...

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