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China Team Selection Test
2021 China Team Selection Test
4
NT function innequality
NT function innequality
Source: 2021ChinaTST test3 day2 P1
April 13, 2021
number theory function
number theory
Innequality
floor function
inequalities
Problem Statement
Proof that
∑
m
=
1
n
5
ω
(
m
)
≤
∑
k
=
1
n
⌊
n
k
⌋
τ
(
k
)
2
≤
∑
m
=
1
n
5
Ω
(
m
)
.
\sum_{m=1}^n5^{\omega (m)} \le \sum_{k=1}^n\lfloor \frac{n}{k} \rfloor \tau (k)^2 \le \sum_{m=1}^n5^{\Omega (m)} .
m
=
1
∑
n
5
ω
(
m
)
≤
k
=
1
∑
n
⌊
k
n
⌋
τ
(
k
)
2
≤
m
=
1
∑
n
5
Ω
(
m
)
.
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