/*
Find sum of sigma(n) where sigma(n) is the sum of the divisors of n.
(Very Fast Program)

Written by P L Patodia on 09.01.2008
Modifie on 25.06.2008 (There was small bug, however this did not affect the value of A072692)
*/
A024916(z) = 
{
  local(s,u,d,n,a,p);
  s = z*z; u = sqrtint(z); p = 0;
  for(d=1, u, 
    n = z\d - z\(d+1); 
    if(n<=1, p=d; break(), a = z%d; s -= (2*a+(n-1)*d)*n/2);
  );
  if(p==0, u=z\(u+1), u=z\p);
  for(d=2, u, s -= z%d);
  return(s);
}

/*
A072692 - Sum of sigma(j) for 1<=j<=10^n, where sigma(j) is the sum of the divisors of j.
*/
A072692(n) = 
{
  for(i=1, n, print(i,": ", A024916(10^i)))
}