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2016 LMT
21
21
Part of
2016 LMT
Problems
(1)
2016 LMT Individual #21
Source:
4/10/2016
Let
S
S
S
be the set of positive integers
n
n
n
such that
3
⋅
φ
(
n
)
=
n
,
3\cdot \varphi (n)=n,
3
⋅
φ
(
n
)
=
n
,
where
φ
(
n
)
\varphi (n)
φ
(
n
)
is the number of positive integers
k
≤
n
k\leq n
k
≤
n
such that
gcd
(
k
,
n
)
=
1
\gcd (k, n)=1
g
cd
(
k
,
n
)
=
1
. Find
∑
n
∈
S
1
n
.
\sum_{n\in S} \, \frac{1}{n}.
n
∈
S
∑
n
1
.
Proposed by Nathan Ramesh