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1400
Totient Product
Editorial
number theory
totient
divisors
Legendre's formula
factorials
Let
f
(
n
)
=
∑
d
∣
n
φ
(
d
)
f(n) = \displaystyle\sum_{d \mid n} \varphi(d)
f
(
n
)
=
d
∣
n
∑
φ
(
d
)
, where
φ
\varphi
φ
denotes Euler's totient function. Find the highest power of
3
3
3
dividing the product
f
(
1
)
⋅
f
(
2
)
⋅
f
(
3
)
⋯
f
(
67
)
.
f(1) \cdot f(2) \cdot f(3) \cdots f(67).
f
(
1
)
⋅
f
(
2
)
⋅
f
(
3
)
⋯
f
(
67
)
.
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