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National and Regional Contests
PEN Problems
PEN A Problems
62
62
Part of
PEN A Problems
Problems
(1)
A 62
Source:
5/25/2007
Let
p
(
n
)
p(n)
p
(
n
)
be the greatest odd divisor of
n
n
n
. Prove that
1
2
n
∑
k
=
1
2
n
p
(
k
)
k
>
2
3
.
\frac{1}{2^{n}}\sum_{k=1}^{2^{n}}\frac{p(k)}{k}> \frac{2}{3}.
2
n
1
k
=
1
∑
2
n
k
p
(
k
)
>
3
2
.
Divisibility Theory