Track / Stage 4 / 103 of 340 #363 of 2000

Problem 363

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

# Problem 1. (2 points)

Do there exist two natural numbers $x$ and $y$ , having the same number of natural divisors, such that $x<y$ , and the sum of all divisors of $x$ (including 1 and the number itself) is greater than the sum of natural divisors of $y$ (including 1 and the number itself)?

Your answer

Official solution

Answer: Yes

Solution:

For example, the numbers 38 and $39: 1+2+19+38=60>56=1+3+13+39$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.