const properDivisors = (n: number): number[] => {
  const divs: number[] = [];
  for (let i = 1; i <= Math.sqrt(n); i++) {
    if (n % i === 0) {
      divs.push(i);
      const otherDivisor = n / i;
      if (otherDivisor !== i && otherDivisor !== n) {
        divs.push(otherDivisor);
      }
    }
  }

  return divs;
}

const sumOfDivisors = (n: number): number => {
  const divs = properDivisors(n)
  return divs.reduce((acc, div) => acc + div, 0);
}

export function buddy(start: number, limit: number): number[] {
  for (let n = start; n <= limit; n++) {
    const sumN = sumOfDivisors(n);
    const m = sumN - 1;
    const sumM = sumOfDivisors(m);
    if (m > n && sumM === n + 1) {
      return [n, m];
    }
  }

  return [];
}