MathDB

Let

r\geq 2

be a positive integer, and let each positive integer be painted in one of

r

different colors. For every positive integer

n

and every pair of colors

a

and

b

, if the difference between the number of divisors of

n

that are painted in color

a

and the number of divisors of

n

that are painted in color

b

is at most

1

, find all possible values of

r

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