func P5(n int64) int64 {
result := int64(1)
for _, p := range eulertools.Primes(n) {
var b int64
for b = p; b*p <= n; b *= p {
}
result *= b
}
return result
}
func P133(n int64) int64 {
//P133(100000)
var result int64
result = 0
for _, p := range eulertools.Primes(n) {
if !is_factor_of_R_n(p) {
result += p
}
}
return result
}