/*
 * Run 'a.out #N' to show, iteratively, the sum of factors of N.
 * Perfect numbers will have cycle 1, amicable cycle 2, etc.
 *
 * Note the efficient caulculation of sum of factors.
 */
 
#include	<stdio.h>
typedef unsigned long long Number;

Number findfact(Number x)
{
	Number  y;

	if (x % 2 == 0) return 2;
	if (x % 3 == 0) return 3;
	if (x % 5 == 0) return 5;
	for (y = 6; y * y < x; y += 6) {
		if (x % (y + 1) == 0) return y + 1;
		if (x % (y + 5) == 0) return y + 5;
	}
	return x;
}

Number fsum(Number x)
{
	Number  y, sum, res, ff, prm;
	int  nf;

	prm = sum = res = ff = 1;
	while (1) {
		y = findfact(x);
		if (y != prm) {
			sum *= res;
			prm = y;
			res = ff = 1;
		}
		if (y < 2)
			return sum;
		res += (ff *= prm);
		x /= y;
	}
}

int main(int argc, char **argv)
{
	long long  m, x;

	setbuf(stdout, 0);
	m = x = argc > 1 ? atol(argv[1]) : 30114860L;
	printf("%Ld -> ", x);
	while (x > 1) {
		x = fsum(x) - x;
		printf("%Lu -> ", x);
		if (x < m)
			m = x;
		else if (x == m || x == 14316)
			break;
	}
	printf("\n");
	return 0;
}