#!/usr/bin/env python3
########################################################################
# Solves problem 124 from projectEuler.net.
# Finds the n of the 10000th rad(n) of the first 100000 rads.
# Copyright (C) 2011 Santiago Alessandri
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
#
# You can contact me at san.lt.ss@gmail.com
# Visit my wiki at http://wiki.san-ss.com.ar
# Visit my blog at http://blog.san-ss.com.ar
########################################################################
from CommonFunctions import find_primes_less_than
LIMIT = 100000
if __name__ == '__main__':
primes = find_primes_less_than(LIMIT)
rads = [[1, i] for i in range(LIMIT+1)]
for p in primes:
for i in range(p, LIMIT+1, p):
rads[i][0] *= p
print("The result is:", sorted(rads)[10000][1])