http://acm.hdu.edu.cn/showproblem.php?pid=6715
Meaning of the questions:
Requirements: \ (\ SUM \ limits_ {I =. 1} ^ {n-} \ SUM \ limits_ {I =. 1} ^ {m} \ MU (LCM (I, J)) \) , where n, m is the range 1e6 the 10 groups.
No, like a long time, I do not know where the fake. Probably the outset wrong direction.
Correct answer:
所求：\(\sum\limits_{i=1}^{n}\sum\limits_{i=1}^{m}\mu(lcm(i,j))\)
即：\(\sum\limits_{i=1}^{n}\sum\limits_{i=1}^{m}\mu(\frac{i*j}{gcd(i,j)})\)
枚举g：\(\sum\limits_{g=1}^{N}\sum\limits_{i=1}^{n}\sum\limits_{i=1}^{m}\mu(\frac{i}{g}*j)[gcd(i,j)==g]\)
Obviously the fact that a: \ (\ MU (XY) = \ MU (X) * \ MU (Y) * [GCD (X, Y) ==. 1] \)
substituting into: \ (\ MU (\ {FRAC i} {g} * j)
= \ mu (\ frac {i} {g}) * \ mu (j) * [gcd (\ frac {i} {g}, j) == 1] \) namely: \ (\ mu (\ frac { i} {g} * j) = \ mu (\ frac {i} {g}) * \ mu (j) \)
Similarly: