Given an integer $n$ find smallest integer $i$ such that $σ(i)=n$. Smallest Inverse Sum of Divisors

Question

Hi All I need some help I am trying to solve this problem which involves computation of sum of divisors and its inverse.

In other words Given an integer $n$ find smallest integer $i$ such that $σ(i)=n$

Explanation about my algorithm. 1 I am finding the sum of Divisor till $10^8$ and the computing its inverse in an hash table and answering each query in $O(1)$ for hast table, But I am getting TLE(Time limit exceeded) The expected running Time is 10s but My code is taking 11s can someone help me with some better approach or some hint how to do this within the given time limit Thanks.

problem link http://www.spoj.com/problems/INVDIV/

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
#define MAX 100000000
#define MAX1 100000000
using namespace std;
unsigned DIV[MAX];
unsigned INVDIV[MAX];
int main()
{

    int tc;unsigned c;
    for (unsigned i=1;i<=10000;i++)
    {
        c=i+1;DIV[i*i]+=i;
        for(int j=i*(i+1);j<MAX1;j+=i) 
        {
            DIV[j]+=i+c;
            c+=1;
        }

    }
    for(unsigned i=2;i<MAX;i++) 
    {
        if (DIV[i]<MAX)
         if (INVDIV[DIV[i]]==0) 
           {
            INVDIV[DIV[i]]=i;
           }
    }
    INVDIV[1]=1;
    int n;
    scanf("%d",&tc);
    while(tc--){
               scanf("%d",&n);
               if(INVDIV[n]!=0)printf("%d\n",INVDIV[n]);
               else printf("-1\n");
    }
    return 0;
}