Data commit

Task/Zumkeller-numbers/Sidef/zumkeller-numbers.sidef

@@ -0,0 +1,34 @@
+func is_Zumkeller(n) {
+
+    return false if n.is_prime
+    return false if n.is_square
+
+    var sigma = n.sigma
+
+    # n must have an even abundance
+    return false if (sigma.is_odd || (sigma < 2*n))
+
+    # true if n is odd and has an even abundance
+    return true if n.is_odd    # conjecture
+
+    var divisors = n.divisors
+
+    for k in (2 .. divisors.end) {
+        divisors.combinations(k, {|*a|
+            if (2*a.sum == sigma) {
+                return true
+            }
+        })
+    }
+
+    return false
+}
+
+say "First 220 Zumkeller numbers:"
+say (1..Inf -> lazy.grep(is_Zumkeller).first(220).join(' '))
+
+say "\nFirst 40 odd Zumkeller numbers: "
+say (1..Inf `by` 2 -> lazy.grep(is_Zumkeller).first(40).join(' '))
+
+say "\nFirst 40 odd Zumkeller numbers not divisible by 5: "
+say (1..Inf `by` 2 -> lazy.grep { _ % 5 != 0 }.grep(is_Zumkeller).first(40).join(' '))