#1808 - Maximize Number of Nice Divisors

Problem Description

You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:

The number of prime factors of n (not necessarily distinct) is at most primeFactors.
The number of nice divisors of n is maximized. Note that a divisor of n is nice if it is divisible by every prime factor of n. For example, if n = 12, then its prime factors are [2,2,3], then 6 and 12 are nice divisors, while 3 and 4 are not.

Return the number of nice divisors of n. Since that number can be too large, return it modulo 109 + 7.

Note that a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. The prime factors of a number n is a list of prime numbers such that their product equals n.

Solution

/**
 * @param {number} primeFactors
 * @return {number}
 */
var maxNiceDivisors = function(primeFactors) {
  const MOD = 1e9 + 7;

  if (primeFactors <= 3) return primeFactors;

  const quotient = Math.floor(primeFactors / 3);
  const remainder = primeFactors % 3;

  if (remainder === 0) return power(3, quotient);
  if (remainder === 1) return (power(3, quotient - 1) * 4) % MOD;

  return (power(3, quotient) * 2) % MOD;

  function power(base, exponent) {
    let result = BigInt(1);
    base = BigInt(base);
    while (exponent > 0) {
      if (exponent & 1) result = (result * base) % BigInt(MOD);
      base = (base * base) % BigInt(MOD);
      exponent >>= 1;
    }
    return Number(result);
  }
};