Data update

Task/Sphenic-numbers/C-sharp/sphenic-numbers.cs

@@ -0,0 +1,62 @@
+using System.Linq;
+using System.Collections.Generic;
+using static System.Console;
+
+public static class SphenicNumbers
+{
+    public static void Main()
+    {
+        var numbers = FindSphenicNumbers(1_000_000).OrderBy(t => t.N).ToList();
+        var triplets = numbers.Select(t => t.N).Consecutive().ToList();
+
+        WriteLine("Sphenic numbers up to 1 000");
+        numbers.Select(t => t.N).TakeWhile(n => n < 1000).Chunk(15)
+            .Select(row => row.Delimit()).ForEach(WriteLine);
+        WriteLine();
+
+        WriteLine("Sphenic triplets up to 10 000");
+        triplets.TakeWhile(n => n < 10_000).Select(n => (n-2, n-1, n)).Chunk(3)
+            .Select(row => row.Delimit()).ForEach(WriteLine);
+        WriteLine();
+
+        WriteLine($"Number of sphenic numbers < 1 000 000: {numbers.Count}");
+        WriteLine($"Number of sphenic triplets < 1 000 000: {triplets.Count}");
+        var (n, (a, b, c)) = numbers[199_999];
+        WriteLine($"The 200 000th sphenic number: {n} = {a} * {b} * {c}");
+        int t = triplets[4_999];
+        WriteLine($"The 5 000th sphenic triplet: {(t-2, t-1, t)}");
+    }
+
+    static IEnumerable<(int N, (int, int, int) Factors)> FindSphenicNumbers(int bound)
+    {
+        var primes = PrimeMath.Sieve(bound / 6).ToList();
+        for (int i = 0; i < primes.Count; i++) {
+            for (int j = i + 1; j < primes.Count; j++) {
+                int p = primes[i] * primes[j];
+                if (p >= bound) break;
+                for (int k = j + 1; k < primes.Count; k++) {
+                    if (primes[k] > bound / p) break;
+                    int n = p * primes[k];
+                    yield return (n, (primes[i], primes[j], primes[k]));
+                }
+            }
+        }
+    }
+
+    static IEnumerable<int> Consecutive(this IEnumerable<int> source)
+    {
+        var (a, b, c) = (0, 0, 0);
+        foreach (int d in source) {
+            (a, b, c) = (b, c, d);
+            if (b - a == 1 && c - b == 1) yield return c;
+        }
+    }
+
+    static string Delimit<T>(this IEnumerable<T> source, string separator = " ") =>
+        string.Join(separator, source);
+
+    static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
+    {
+        foreach (T element in source) action(element);
+    }
+}

Task/Sphenic-numbers/Sidef/sphenic-numbers.sidef

@@ -0,0 +1,26 @@
+func sphenic_numbers(upto) {
+    3.squarefree_almost_primes(upto)
+}
+
+func sphenic_triplets(upto) {
+    var S = sphenic_numbers(upto)
+    S.grep_kv {|k,v| v+2 == S[k+2] }.map{ [_, _+1, _+2] }
+}
+
+with (1e3) {|n|
+    say "Sphenic numbers less than #{n.commify}:"
+    sphenic_numbers(n-1).slices(15).each{.map{'%4s' % _}.join.say}
+}
+
+with (1e4) {|n|
+    say "\nSphenic triplets less than #{n.commify}:"
+    sphenic_triplets(n-1).each{.say}
+}
+
+with (1e6) {|n|
+    var triplets = sphenic_triplets(n-1)
+    say "\nThere are #{3.squarefree_almost_prime_count(n-1)} sphenic numbers less than #{n.commify}."
+    say "There are #{triplets.len} sphenic triplets less than #{n.commify}."
+    with (2e5) {|n| say "The #{n.commify}th sphenic number is: #{nth_squarefree_almost_prime(n, 3)}." }
+    with (5e3) {|n| say "The #{n.commify}th sphenic triplet is: #{triplets[n-1]}." }
+}