MathDB

2015 Advanced #4

Source:

July 8, 2022

2015Advanced Topics Test

Problem Statement

Given a positive integer

x>1

with

n

divisors, define

f(x)

to be the product of the smallest

\lceil\tfrac{n}{2}\rceil

divisors of

x

. Let

a

be the least value of

x

such that

f(x)

is a multiple of

X

, and

b

be the least value of

n

such that

f(y)

is a multiple of

y

for some

y

that has exactly

n

factors. Compute

a+b

.

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