Just another update

Task/Arithmetic-Rational/Groovy/arithmetic-rational-4.groovy

@@ -0,0 +1,25 @@
+Number.metaClass.mixin RationalCategory
+
+def factorize = { target ->
+    assert target > 0
+    if (target == 1L) { return [1L] }
+    if ([2L, 3L].contains(target)) { return [1L, target] }
+    def targetSqrt = Math.sqrt(target)
+    def lowFactors = (2L..targetSqrt).findAll { (target % it) == 0 }
+
+    if (!lowFactors) { return [1L, target] }
+    def highFactors = lowFactors[-1..0].findResults { target.intdiv(it) } - lowFactors[-1]
+
+    return [1L] + lowFactors + highFactors + [target]
+}
+
+def perfect = {
+    def factors = factorize(it)
+    2 as Rational == factors.sum{ factor -> new Rational(1, factor) } \
+        ? [perfect: it, factors: factors]
+        : null
+}
+
+def trackProgress = { if ((it % (100*1000)) == 0) { println it } else if ((it % 1000) == 0) { print "." } }
+
+(1..(2**19)).findResults { trackProgress(it); perfect(it) }.each { println(); print it }