#include <stdio.h>
/*** New outputformat & 2 start parameter supported:  2002-11-07  (C) GPL ***/
/*** Author: Achim Flammenkamp, University of Bielefeld, achim@uni-bielefeld.de
     Reference: Collected Papers of Srinivasa Ramanujan (1927), chapter 15:
                Highly Composite Numbers  p. 78-128, paragraph 2-31 p. 81-111
******************************************************************************/
#ifndef  N
#define  N  (1<<8)
#endif
double  lnp[N];


init_prime_logs()
{
   unsigned  h, i, j, k;
   extern double log(double);
   lnp[h=0]= 2;
   for (k=1,i=3;k<N;i+=2)
   {
      if (lnp[h]*lnp[h] <= i)
         h++;
      for (j=1;j<h;j++)
         if (!(i % (unsigned)lnp[j]))  break;
      if (j >= h)
         lnp[k++] = i;
   }
   for (k=0;k<N;k++)
      lnp[k]= log( lnp[k] );
}


print_composite(unsigned k, double vval, double dd, unsigned f[], unsigned nn)
{
   unsigned  h, i;
   printf("%5u  %15.10lf  ",k, vval);
   if (dd < 1e14)
      printf("%14.0lf  ", dd);
   else
      printf("%14.8le  ", dd);
   h=0;
   printf("%3u  ",nn);
   for (i=0;i<nn;i++)
      if (!i || f[i] != f[i-1])
      {  if (h)
            printf("^%u",h+1);
         h=0;
         printf("%2u",f[i]);
      }
      else
         h++;
   if (h)
      printf("^%u ",h+1);
   printf("\n");
}


int main(unsigned argc, char *argv[])
{

unsigned  h, i, j, k, n, e[N], f[N];
unsigned  en, nn;
double  last, dl, max, val, d, dd, vval;

init_prime_logs();
setlinebuf(stdout);

vval=0.0;
dd= 1.0;
if (argc > 1 && 1 != sscanf(argv[1],"%lf",&vval))
   exit( printf("usage: %s [ln_minimal_number [at_least_d]]\n",argv[0]), 1);
if (argc > 2 && (1 != sscanf(argv[2],"%lf",&dd) || dd <= 0.0))
   exit( printf("usage: %s [ln_minimal_number [at_least_d]]\n",argv[0]), 1);

for (i=0;i<N;i++)
   e[i]=0;
n=nn=0;
for (k=0;n<N;k++)
{
   print_composite(k, vval, dd, f, nn);
   last=vval;
   max= last + 0.6931471805599453;  /** ln(2); **/
   dl= dd;
   vval= max;
   for (i=0;i<n;i++)
      e[i]=0;
   n=1;
   val= 0.0;
   d = 1.0;
   do {
      i=0;
      do {
         while (e[i]+1 > 2*(unsigned)(lnp[n]/lnp[i]))
            i++;
         if (i==n)  n++;
         en= e[i]+1;
         for (j=0;j<=i;j++)
         {
            val -= e[j]*lnp[j];
            d /= e[j]+1;
            e[j]=en;
            if ((en+1)*lnp[j] < lnp[n-1])
               e[j]= lnp[n-1]/lnp[j];
            val += e[j]*lnp[j];
            d *= e[j]+1;
         }
         if (val > vval && en==1)  goto done;
         i++;
      } while (val > vval); 
      if (val > last && d > dl*(1.0+1e-12))
      {
         dd= d;
         vval= val;
         nn=n;
         for (i=0;i<n;i++)
            f[i]=e[i];
      }
   } while (1);
   done: 
}
return 0;
}