【BZOJ2440】完全平方数（莫比乌斯函数，容斥原理）

题意：求第k个无平方因子数

k<=10^9

思路：

感觉这东西和欧拉筛差不多……活到老学到老，退役前学点新知识也是好的

为什么二分答案的上界是2*n？连LYY都证不出来

话说约大爷一年之前就已经AC此题……%%%

const max=50000;
var mu,flag,prime:array[1..max]of int64;
    cas,v,i,m,j,n:longint;
    ans,l,r,mid,last,tmp:int64;

function clac(n:int64):int64;
var i:longint;
begin
 clac:=0;
 for i:=1 to trunc(sqrt(n)) do clac:=clac+mu[i]*n div (i*i);
end;

begin
 assign(input,'bzoj2440.in'); reset(input);
 assign(output,'bzoj2440.out'); rewrite(output);
 readln(cas);
 mu[1]:=1;
 for i:=2 to max do
 begin
  if flag[i]=0 then
  begin
   inc(m); prime[m]:=i;
   mu[i]:=-1;
  end;
  j:=1;
  while prime[j]*i<=max do
  begin
   flag[prime[j]*i]:=1;
   if i mod prime[j]=0 then
   begin
    mu[prime[j]*i]:=0;
    break;
   end;
   mu[prime[j]*i]:=-mu[i];
   inc(j);
  end;
 end;
 for v:=1 to cas do
 begin
  readln(n);
  l:=1; r:=2*n; last:=1;
  while l<=r do
  begin
   mid:=(l+r)>>1;
   tmp:=clac(mid);
   if tmp=n then begin last:=mid; r:=mid-1; end
    else if tmp<n then l:=mid+1
     else r:=mid-1;
  end;
  writeln(last);
 end;
 close(input);
 close(output);
end.