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PEN J Problems
19
J 19
J 19
Source:
May 25, 2007
Divisor Functions
Problem Statement
Prove that
σ
(
n
)
ϕ
(
n
)
<
n
2
\sigma(n)\phi(n) < n^2
σ
(
n
)
ϕ
(
n
)
<
n
2
, but that there is a positive constant
c
c
c
such that
σ
(
n
)
ϕ
(
n
)
≥
c
n
2
\sigma(n)\phi(n) \ge c n^2
σ
(
n
)
ϕ
(
n
)
≥
c
n
2
holds for all positive integers
n
n
n
.
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