MathDB

Let

a_{1}=1

a_{2}=2

a_{3}

a_{4}

\cdots

be the sequence of positive integers of the form

2^{\alpha}3^{\beta}

, where

\alpha

and

\beta

are nonnegative integers. Prove that every positive integer is expressible in the form

a_{i_{1}}+a_{i_{2}}+\cdots+a_{i_{n}},

where no summand is a multiple of any other.

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