HTML Code

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <title>Smith number trace</title>
</head>
<body>
  <h1>Trace S(n) and F(n)</h1>
  <p>Edit <code>candidates</code>, then <strong>Run</strong>.</p>
  <pre id="out"></pre>
  <script>
    (function () {
      function digitSum(n) {
        var total = 0;
        while (n > 0) {
          total += n % 10;
          n = Math.floor(n / 10);
        }
        return total;
      }
      function isPrime(n) {
        if (n <= 1) return false;
        if (n === 2) return true;
        if (n % 2 === 0) return false;
        var i;
        for (i = 3; i * i <= n; i += 2) {
          if (n % i === 0) return false;
        }
        return true;
      }
      function factorDigitSum(n) {
        var total = 0;
        var x = n;
        var i;
        for (i = 2; i * i <= x; i++) {
          while (x % i === 0) {
            total += digitSum(i);
            x = Math.floor(x / i);
          }
        }
        if (x > 1) total += digitSum(x);
        return total;
      }
      function isSmith(n) {
        if (n <= 1 || isPrime(n)) return false;
        return digitSum(n) === factorDigitSum(n);
      }
      var candidates = [4, 7, 15, 27, 85];
      var lines = [];
      var j;
      for (j = 0; j < candidates.length; j++) {
        var n = candidates[j];
        var S = digitSum(n);
        var F = factorDigitSum(n);
        var label = isSmith(n) ? "Smith" : "not Smith";
        lines.push(n + ": S=" + S + ", F=" + F + " -> " + label);
      }
      document.getElementById("out").textContent = lines.join("\n");
    })();
  </script>
</body>
</html>

Lines: 0 | Characters: 0

Live Preview Auto-refresh on Run

JavaScript Smith Number — Trace S(n) and F(n) (Try It)