Checks if a number is perfect

isPerfect.js

// Every perfect number is represented as p one bits followed by (p - 1) zero bits,
// where p is a Mersenne prime.
// Let x be the largest `MAX_BITS`-bit perfect number. Then ceil(log2(x)) = p + (p - 1).
const MAX_BITS = 32; // Bitwise operators operate on 32-bit integers
const MAX_ONES = Math.floor((MAX_BITS + 1) / 2); // upper bound on p

// Precomputed list of all prime m <= p s.t. 2^m - 1 is prime.
// TODO Compute automatically.
const MERSENNE_EXPS = new Set([2, 3, 5, 7, 13]);

function isPerfect(n) {
  // Iterate through initial (p - 1) zeros.
  let p;
  for (p = 1; !(n & 1) && p < MAX_ONES; p++) {
    n >>= 1;
  }

  // If the given value is perfect, n is now (2^p - 1).
  if (n !== ((1 << p) - 1)) {
    return false;
  }
  return MERSENNE_EXPS.has(p);
}

test.js

// https://oeis.org/A000396
[6, 28, 496, 8128, 33550336].forEach(n => {
  if (!isPerfect(n)) {
    console.log(`isPerfect returned false for perfect n=${n}`);
  }
});

[
  // Some pernicious numbers (https://oeis.org/A052294)
  3, 5, 7, 9, 10, 11, 12, 26, 2096128,
  // Other non-perfect numbers
  0, 1, 2, 4, 8, 13, 27, 130816
].forEach(n => {
  if (isPerfect(n)) {
    console.log(`isPerfect returned true for non-perfect n=${n}`);
  }
});