Track / Stage 4 / 116 of 340 #856 of 2444

Problem 856

AMC 12 late, AIME early

Number theory Difficulty 4.6 Find the answer HMMT February

Find the sum of the reciprocals of all the (positive) divisors of 144.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

As $d$ ranges over the divisors of 144 , so does $144 / d$ , so the sum of $1 / d$ is $1 / 144$ times the sum of the divisors of 144 . Using the formula for the sum of the divisors of a number (or just counting them out by hand), we get that this sum is 403, so the answer is 403/144.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.