Luo Gu $ P $ 2522 $ Problem \ b \ [HAOI2011] $ Mobius inversion

Positive Solutions: Mobius inversion

Report problem solving:

Portal!

First we saw this apparently thought Mobius inversion $ QwQ $?

Messing around on the first chant at $ QwQ $

$gcd(x,y)=k$,即$gcd(\left \lfloor \frac{x}{k} \right \rfloor,\left \lfloor \frac{y}{k} \right \rfloor)=1$

Then this, although several times before pushing hot ,,, but still pushed down again ,,, too long did not touch these things spicy / $ kel \ kel \ kel $

Provided $ F [k] $ represents $ gcd (x, y) $ is the number of $ k $ multiples apparently a $ F [k] = \ left \ lfloor \ frac {a} {k} \ right \ rfloor \ cdot \ left \ lfloor \ frac {b} {k} \ right \ rfloor $

Then set $ f [x] $ represents $ gcd (x, y) = k $ the number, it is clear that there is $ F [k] = \ sum_ {k | d} f [d] $

Then directly on the hot Mobius inversion on Eau ,,, $ f [k] = \ sum_ {k | d} \ mu (\ frac {k} {d}) \ cdot F [d] $.

Then the inquiry $ a \ leq x \ leq b, c \ leq y \ leq d $, apparently find the $ x \ leq b, y \ leq d $ & $ x \ leq b, y \ leq c $ & $ x \ leq a, y \ leq d $ & $ x \ leq a, y \ leq c $, then the receiving blind-repellent finish on hot ,,, $ QwQ $

Then look at the complexity of the look but also the number estimated on the block ,,,? I do not know anyway, plus the number of points on the block apparently no loss hee hee, then add $ QwQ $ chant

$ Over $, $ QAQ $ codes and other decentralized