MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN J Problems
21
21
Part of
PEN J Problems
Problems
(1)
J 21
Source:
5/25/2007
Show that for any positive integer
n
n
n
,
σ
(
n
!
)
n
!
≥
∑
k
=
1
n
1
k
.
\frac{\sigma(n!)}{n!}\ge \sum_{k=1}^{n}\frac{1}{k}.
n
!
σ
(
n
!)
≥
k
=
1
∑
n
k
1
.
Divisor Functions