dtoj1836老逗的gcd(gcd)

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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;">众所周知，老逗是数学之王。</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;"></span>
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;">今天老逗的数学老师教了关于</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">gcd</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">的知识。所谓两个数的</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">gcd</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">，就是能同时整除这两个数</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;"></span>
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;">的最大的正整数。作为课后练习，老师随手掏出两个数字</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">n</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">和</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">m</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">，要求同学们算出</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">1</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">到</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">n</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">中所</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;"></span>
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;">有数与</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">1</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">到</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">m</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">中所有数的</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">gcd</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">之和。但是老逗对于这种愚蠢的行为深恶痛绝，所以，对于一个</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;"></span>
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;">可以被一个完全平方数</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">k</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">整除（</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">k > 1</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">）的</span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;">gcd</span><span style="font-size:12.0pt;line-height:150%;font-family:宋体;">，老逗是不屑于把它加到答案里去的。你知道老逗算出的答案是多少吗？</span>
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对于给定的 $ n,m $ ,求 $ \sum_{i=1}^n{\sum_{j=1}^m{f(i,j)}} $
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其中，函数 $ f(x,y) $ 的定义为：
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;"><img src="http://47.74.229.197/wp-content/uploads/syzoj_pic/upload/201403/3.png" width="614" height="166" alt="" /><br />
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<span style="font-size:12.0pt;line-height:150%;font-family:宋体;"><span> </span></span><span style="font-size:12.0pt;line-height:150%;font-family:Consolas;"></span>
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