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Brazil Undergrad MO
2021 Brazil Undergrad MO
Problem 4
Problem 4
Part of
2021 Brazil Undergrad MO
Problems
(1)
What is the mean of exponents of all naturals?
Source: Brazilian Undergrad MO 2022 Problem 4
5/12/2022
For every positive integeer
n
>
1
n>1
n
>
1
, let
k
(
n
)
k(n)
k
(
n
)
the largest positive integer
k
k
k
such that there exists a positive integer
m
m
m
such that
n
=
m
k
n = m^k
n
=
m
k
.Find
l
i
m
n
→
∞
∑
j
=
2
j
=
n
+
1
k
(
j
)
n
lim_{n \rightarrow \infty} \frac{\sum_{j=2}^{j=n+1}{k(j)}}{n}
l
i
m
n
→
∞
n
∑
j
=
2
j
=
n
+
1
k
(
j
)
real analysis
limits
mean
Exponents
Brazilian Undergrad MO 2021