Integer#franel: Add

lib/numb/franel.rb

@@ -0,0 +1,6 @@
+# coding: utf-8
+class Integer
+  def franel
+    (0..self).map{|k| choose(k) ** 3 }.reduce(:+)
+  end
+end

lib/numb/number_of_divisors.rb

@@ -5,6 +5,8 @@ class Integer
 
   # Returns the number of divisors of self
   def τ 
+    # TODO: Consider something simpler, and perhaps faster, like
+    # primaries.map(&:last).map(&:succ).reduce(:*)
     n = self
     return @nod if defined?(@nod)
     @nod = (1..isqrt).

spec/numb/franel_spec.rb

@@ -0,0 +1,15 @@
+# coding: utf-8
+describe Integer, "#franel" do
+  # A000172
+  @seq = [1,2,10,56,346,2252,15184,104960,739162,5280932,
+          38165260,278415920,2046924400,15148345760,
+          112738423360,843126957056,6332299624282,
+          47737325577620,361077477684436,2739270870994736,
+          20836827035351596]
+
+  @seq.each_with_index do |franel, n|
+    it "returns #{franel} for #{n}" do
+      n.franel.should == franel
+    end
+  end
+end