MathDB

Math Prize 2016 Problem 17

Source:

September 12, 2016

Math Prize for Girls

Problem Statement

We define the weight

W

of a positive integer as follows:

W(1) = 0

W(2) = 1

W(p) = 1 + W(p + 1)

for every odd prime

p

W(c) = 1 + W(d)

for every composite

c

, where

d

is the greatest proper factor of

c

. Compute the greatest possible weight of a positive integer less than 100.