Add Aliquot sum (#18)

.spec/math/aliquot_sum_spec.lua

@@ -0,0 +1,35 @@
+describe("Aliquot sum", function()
+	local aliquot_sum = require("math.aliquot_sum")
+
+	it("should handle general cases", function()
+		assert.equal(0, aliquot_sum(1))
+		assert.equal(1, aliquot_sum(2))
+		assert.equal(1, aliquot_sum(3))
+		assert.equal(1 + 2, aliquot_sum(4))
+		assert.equal(1, aliquot_sum(5))
+		assert.equal(1 + 2 + 3, aliquot_sum(6))
+		assert.equal(1, aliquot_sum(7))
+		assert.equal(1 + 2 + 4, aliquot_sum(8))
+		assert.equal(1 + 3, aliquot_sum(9))
+		assert.equal(106, aliquot_sum(80))
+		assert.equal(114, aliquot_sum(102))
+		assert.equal(312, aliquot_sum(168))
+		assert.equal(14, aliquot_sum(169))
+		assert.equal(154, aliquot_sum(170))
+		assert.equal(89, aliquot_sum(171))
+		assert.equal(533, aliquot_sum(1771))
+		assert.equal(7044, aliquot_sum(7852))
+	end)
+
+	it("should throw error when input is 0", function()
+		assert.has_error(function()
+			aliquot_sum(0)
+		end)
+	end)
+
+	it("should throw error when input is negative", function()
+		assert.has_error(function()
+			aliquot_sum(-1)
+		end)
+	end)
+end)

src/math/aliquot_sum.lua

@@ -0,0 +1,21 @@
+-- Computes the sum of proper divisors
+-- of the input number of n, i.e.
+-- sum of divisors of n that are less than n.
+return function(n)
+	assert(n > 0, "input must be positive")
+	if n == 1 then
+		return 0
+	end
+	local res = 1
+	for i = 2, math.sqrt(n) do
+		if n % i == 0 then
+			res = res + i
+			local complement = n / i
+			-- Ensure that the same divisor is not counted twice
+			if complement ~= i then
+				res = res + complement
+			end
+		end
+	end
+	return res
+end