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2015 CHMMC (Fall)
8
2015 Fall Team #8
2015 Fall Team #8
Source:
March 26, 2022
floor function
algebra
number theory
Problem Statement
Let
f
(
n
)
=
∑
d
=
1
n
⌊
n
d
⌋
f(n) = \sum^n_{d=1} \left\lfloor \frac{n}{d} \right\rfloor
f
(
n
)
=
∑
d
=
1
n
⌊
d
n
⌋
and
g
(
n
)
=
f
(
n
)
−
f
(
n
−
1
)
g(n) = f(n) -f(n - 1)
g
(
n
)
=
f
(
n
)
−
f
(
n
−
1
)
. For how many
n
n
n
from
1
1
1
to
100
100
100
inclusive is
g
(
n
)
g(n)
g
(
n
)
even?
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