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2023 Harvard-MIT Mathematics Tournament
1
HMMT Feb 2023 Team p1
HMMT Feb 2023 Team p1
Source:
February 20, 2023
Problem Statement
For any positive integer
a
a
a
, let
τ
(
a
)
\tau(a)
τ
(
a
)
be the number of positive divisors of
a
a
a
. Find, with proof, the largest possible value of
4
τ
(
n
)
−
n
4\tau(n)-n
4
τ
(
n
)
−
n
over all positive integers
n
n
n
.
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