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Montgomery Blair
MBMT Team Rounds
2020.43
2020.43
Part of
MBMT Team Rounds
Problems
(1)
\sigma_k(n)/ n^{k+2} (2020n + 2019)^2 > m 2020 MBMT p43
Source:
2/13/2022
Let
σ
k
(
n
)
\sigma_k(n)
σ
k
(
n
)
be the sum of the
k
t
h
k^{th}
k
t
h
powers of the divisors of
n
n
n
. For all
k
≥
2
k \ge 2
k
≥
2
and all
n
≥
3
n \ge 3
n
≥
3
, we have that
σ
k
(
n
)
n
k
+
2
(
2020
n
+
2019
)
2
>
m
.
\frac{\sigma_k(n)}{n^{k+2}} (2020n + 2019)^2 > m.
n
k
+
2
σ
k
(
n
)
(
2020
n
+
2019
)
2
>
m
.
Find the largest possible value of
m
m
m
.
number theory
MBMT