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package factors
// Totient calculates the number of numbers less than n that
// are totatives of n (share no factors with n)
func Totient(n uint) uint {
if n == 0 {
return 0
}
primeFactorization := PrimeFactorize(n)
num, denom := uint(1), uint(1)
for p := range primeFactorization.exponents {
num *= p - 1
denom *= p
}
return num * (n / denom)
}
// TotativeDigits returns a slice containing every number less than r
// that is a totative of r (shares no factors with r).
func TotativeDigits(r uint32) []uint32 {
digits := make([]uint32, Totient(uint(r)))
totativesFound := 0
for d := uint32(0); d < r; d++ {
if gcd(d, r) == 1 {
digits[totativesFound] = d
totativesFound++
}
}
return digits
}
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