MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN J Problems
19
19
Part of
PEN J Problems
Problems
(1)
J 19
Source:
5/25/2007
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
.
Divisor Functions