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1.2
1.2
Part of
2018 PUMaC Live Round
Problems
(1)
2018 PUMaC Live Round 1.2
Source:
1/13/2019
Define a function given the following
2
2
2
rules:
\qquad
1) for prime
p
p
p
,
f
(
p
)
=
p
+
1
f(p)=p+1
f
(
p
)
=
p
+
1
.
\qquad
2) for positive integers
a
a
a
and
b
b
b
,
f
(
a
b
)
=
f
(
a
)
⋅
f
(
b
)
f(ab)=f(a)\cdot f(b)
f
(
ab
)
=
f
(
a
)
⋅
f
(
b
)
. For how many positive integers
n
≤
100
n\leq 100
n
≤
100
is
f
(
n
)
f(n)
f
(
n
)
divisible by
3
3
3
?
function
PuMAC
Live Round