Build a drug testing scheduler
Javascript 5,955,958,211

I'm not sure if it is the optimal solution.
I used a brute-force method.



function f(n) {
  var o=[];
  for(var i=n;i--;) o.push(2*n-i); //init array from n+1 to 2*n

  for(i=n;i&gt;0;i--) { //bruteforce on number from n to 1
    var index=0;
    var nbFactor=0;
    for(j=0;j&lt;n;j++) {
      if((o[j]/i)%1==0) {
        index=j;
        nbFactor++;
      }
    }
    if(nbFactor==1) { //if there is only 1 factor, replace it by the new number
      o[index]=i;
    }
  }
  return o.sort(function(a,b){return a-b;});
}


Golfed (130) :

function f(n){o=[];for(i=n;i++&lt;2*n;)o.push(i);for(i=n;i;i--){for(d=c=j=0;j&lt;n;j++)if((o[j]/i)%1==0)d=j,c++;if(c==1)o[d]=i}return o}


Here is the result found by my algorithm for 25 :  


  [8, 12, 14, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]


Little piece of code to compute the score (takes approx. 200 seconds on Chrome) :

var result=0;
var t = Date.now();
for(var j=1;j&lt;2501;j++) {
  result += f(j).reduce(function(r,e){return r+e;});
}
console.log("Score : " + result + "\nCompute time : " + ((Date.now()-t)/1000) + " seconds");