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LMT
2020 LMT Spring
15
15
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 15
Source:
8/22/2020
Let
ϕ
(
k
)
\phi(k)
ϕ
(
k
)
denote the number of positive integers less than or equal to
k
k
k
that are relatively prime to
k
k
k
. For example,
ϕ
(
2
)
=
1
\phi(2)=1
ϕ
(
2
)
=
1
and
ϕ
(
10
)
=
4
\phi(10)=4
ϕ
(
10
)
=
4
. Compute the number of positive integers
n
≤
2020
n \leq 2020
n
≤
2020
such that
ϕ
(
n
2
)
=
2
ϕ
(
n
)
2
\phi(n^2)=2\phi(n)^2
ϕ
(
n
2
)
=
2
ϕ
(
n
)
2
.