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India LIMIT
2020 LIMIT
2020 LIMIT Category 2
14
n=\sum_{d|n} f(d), f(100)
n=\sum_{d|n} f(d), f(100)
Source: LIMIT 2020 Cat 2 Obj P14
June 9, 2020
Sum
number theory
limit
Problem Statement
Let
f
:
N
→
N
f: N \to N
f
:
N
→
N
satisfy
n
=
∑
d
∣
n
f
(
d
)
,
∀
n
∈
N
n=\sum_{d|n} f(d), \forall n \in N
n
=
∑
d
∣
n
f
(
d
)
,
∀
n
∈
N
. Then sum of all possible values of
f
(
100
)
f(100)
f
(
100
)
is?
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