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Math Prize For Girls Problems
2016 Math Prize for Girls Problems
17
17
Part of
2016 Math Prize for Girls Problems
Problems
(1)
Math Prize 2016 Problem 17
Source:
9/12/2016
We define the weight
W
W
W
of a positive integer as follows:
W
(
1
)
=
0
W(1) = 0
W
(
1
)
=
0
,
W
(
2
)
=
1
W(2) = 1
W
(
2
)
=
1
,
W
(
p
)
=
1
+
W
(
p
+
1
)
W(p) = 1 + W(p + 1)
W
(
p
)
=
1
+
W
(
p
+
1
)
for every odd prime
p
p
p
,
W
(
c
)
=
1
+
W
(
d
)
W(c) = 1 + W(d)
W
(
c
)
=
1
+
W
(
d
)
for every composite
c
c
c
, where
d
d
d
is the greatest proper factor of
c
c
c
. Compute the greatest possible weight of a positive integer less than 100.
Math Prize for Girls