MathDB

Let

a , b , c

positive integers, coprime. For each whole number

n \ge 1

, we denote by

s ( n )

the number of elements in the set

\{ a , b , c \}

that divide

n

. We consider

k_1< k_2< k_3<...

.the sequence of all positive integers that are divisible by some element of

\{ a , b , c \}

. Finally we define the characteristic sequence of

( a , b , c )

like the succession

s ( k_1) , s ( k_2) , s ( k_3) , ....

. Prove that if the characteristic sequences of

( a , b , c )

and

( a', b', c')

are equal, then

a = a', b = b'

and

c=c'

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