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Alexander has chosen a natural number

N>1

and has written down in a line,and in increasing order,all his positive divisors

d_1<d_2<\ldots <d_s

(where

d_1=1

and

d_s=N

).For each pair of neighbouring numbers,he has found their greater common divisor.The sum of all these

s-1

numbers (the greatest common divisors) is equal to

N-2

.Find all possible values of

N

Problem Statement