E. Number Challenge(清晰地推式子)
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E. Number Challenge
问题： ∑ i = 1 a ∑ j = 1 b ∑ k = 1 c d ( i j k ) \\sum_{i=1}^a\\sum_{j=1}^b\\sum_{k=1}^cd(ijk) ∑i=1a∑j=1b∑k=1cd(ijk)， d ( n ) d(n) d(n)表示n的因子个数。
推式子：
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\\sum_{i=1}^a\\sum_{j=1}^b\\sum_{k=1}^cd(ijk)\\\\ \\sum_{i=1}^a\\sum_{j=1}^b\\sum_{k=1}^c\\sum_{x|i}\\sum_{y|j}\\sum_{z|k}[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{x=1}^a\\sum_{y=1}^b\\sum_{z=1}^c\\sum_{i=1}^a\\sum_{j=1}^b\\sum_{k=1}^c\\sum_{x|i}\\sum_{y|j}\\sum_{z|k}[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{x=1}^a\\sum_{y=1}^b\\sum_{z=1}^c\\lfloor\\frac ax\\rfloor\\lfloor\\frac by\\rfloor\\lfloor\\frac cz\\rfloor[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{x=1}^a\\sum_{y=1}^b\\sum_{z=1}^c\\lfloor\\frac ax\\rfloor\\lfloor\\frac by\\rfloor\\lfloor\\frac cz\\rfloor\\sum_{d|gcd(x,y)}\\mu(d)[gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{d=1}^{min(a,b)}\\sum_{x=1}^a\\sum_{y=1}^b\\sum_{z=1}^c\\lfloor\\frac ax\\rfloor\\lfloor\\frac by\\rfloor\\lfloor\\frac cz\\rfloor\\sum_{d|gcd(x,y)}\\mu(d)[gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{d=1}^{min(a,b)}\\mu(d)\\sum_{x=1,d|x}^a\\sum_{y=1,d|y}^b\\sum_{z=1}^c\\lfloor\\frac ax\\rfloor\\lfloor\\frac by\\rfloor\\lfloor\\frac cz\\rfloor[gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{d=1}^{min(a,b)}\\mu(d)\\sum_{x=1}^{\\lfloor\\frac ad\\rfloor}\\sum_{y=1}^{\\lfloor\\frac bd\\rfloor}\\sum_{z=1}^c\\lfloor\\frac a{dx}\\rfloor\\lfloor\\frac b{dy}\\rfloor\\lfloor\\frac cz\\rfloor[gcd(y,z)=1][gcd(x,z)=1]\\\\ \\sum_{d=1}^{min(a,b)}\\mu(d)\\sum_{z=1}^c\\sum_{x=1}^{\\lfloor\\frac ad\\rfloor}[gcd(x,z)=1]\\lfloor\\frac a{dx}\\rfloor\\sum_{y=1}^{\\lfloor\\frac bd\\rfloor}\\lfloor\\frac b{dy}\\rfloor\\lfloor\\frac cz\\rfloor[gcd(y,z)=1]\\\\
i=1∑aj=1∑bk=1∑cd(ijk)i=1∑aj=1∑bk=1∑cx∣i∑y∣j∑z∣k∑[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]x=1∑ay=1∑bz=1∑ci=1∑aj=1∑bk=1∑cx∣i∑y∣j∑z∣k∑[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]x=1∑ay=1∑bz=1∑c⌊xa⌋⌊yb⌋⌊zc⌋[gcd(x,y)=1][gcd(y,z)=1][gcd(x,z)=1]x=1∑ay=1∑bz=1∑c⌊xa⌋⌊y[HDOJ6172] Array Challenge（线性递推，黑科技）
Codeforces 235 E Number Challenge
codeforces 235E Number Challenge