Add totative ratio and factor score to program

1 files changed, 28 insertions, 0 deletions

diff --git a/factors/score.go b/factors/score.go
new file mode 100644
index 0000000..707120d
--- /dev/null
+++ b/factors/score.go
@@ -0,0 +1,28 @@
+package factors
+
+// Score returns a "factor score" equal to the sum of the reciprocoals
+// of the number n's factors.
+// Rationale:
+// A number's factors are one of the most important things that determines
+// how well it functions as a number base.  An easy way to determine how
+// good these factors are is to simply count them, but that comes with
+// the problem that all factors are considered equal when they really aren't
+// - divisibility by 2 (which ensures 1/2 is a terminating fraction and
+// you can tell whether a number is even or odd by looking at the last digit)
+// is more important than divisibility by 23.  The most obvious way of
+// accounting for this is by giving each factor a score and adding those
+// scores to get the overall score.  I chose score(f) = 1/f because it is
+// the simplest function that captures the intuition that smaller factors
+// are more valuable than larger ones.  It also gives the score a meaning:
+// a factor's score is the probability a random number is divisible by it.
+func Score(n uint) float64 {
+	if n == 0 {
+		panic("Cannot get factor score of 0.")
+	}
+
+	factorSum := uint(0)
+	for _, f := range Factors(n) {
+		factorSum += f
+	}
+	return float64(factorSum) / float64(n)
+}