Add totative digit count to non-compact output

This is done for a few reasons:
- Allow the user to easily determine the exact value of the totative
  ratio
- This information is important when the digit map isn't accessible (for
  radices >36)
- More consistency with factors

I don't show the exact values of totatives like I do with factors
because they're far more common - the superior highly composite (i.e.
one of the numbers with the highest factor count) number 720720 has
240 factors and 138240 totatives, for example.

2 files changed, 22 insertions, 2 deletions

diff --git a/factors/factors_test.go b/factors/factors_test.go
index 8373ede..6b56e25 100644
--- a/factors/factors_test.go
+++ b/factors/factors_test.go
@@ -71,6 +71,15 @@ func TestTotativeRatio(t *testing.T) {
 	tableTest(t, TotativeRatio, totativeRatioCases, stdEquals, "TotativeRatio")
 }
 
+var totativeCountCases = map[uint]uint{
+	1: 1, 2: 1, 3: 2, 4: 2, 6: 2, 7: 6, 8: 4, 12: 4,
+	14: 6, 15: 8, 30: 8, 60: 16, 120: 32,
+}
+
+func TestTotativeCount(t *testing.T) {
+	tableTest(t, TotativeCount, totativeCountCases, stdEquals, "TotativeCount")
+}
+
 var factorScoreCases = map[uint]float64{
 	1:   1.0,
 	2:   1.5,
diff --git a/factors/totative.go b/factors/totative.go
index 3a1f635..7a4bebe 100644
--- a/factors/totative.go
+++ b/factors/totative.go
@@ -1,12 +1,22 @@
 package factors
 
-// TotativeRatio calculates the fraction of numbers less than n that
+// TotativeRatio calculates the fraction of numbers that
 // are totatives of n (share no factors with n)
 func TotativeRatio(n uint) float64 {
 	if n == 0 {
 		panic("0 has no totative ratio!")
 	}
 
+	return float64(TotativeCount(n)) / float64(n)
+}
+
+// TotativeCount calculates the number of numbers less than n that
+// are totatives of n (share no factors with n)
+func TotativeCount(n uint) uint {
+	if n == 0 {
+		return 0
+	}
+
 	primeFactorization := PrimeFactorize(n)
 	num, denom := uint(1), uint(1)
 
@@ -14,5 +24,6 @@ func TotativeRatio(n uint) float64 {
 		num *= p - 1
 		denom *= p
 	}
-	return float64(num) / float64(denom)
+
+	return num * (n / denom)
 }