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Define a a sequence {<{a_n}>}^{\infty}_{n\equal{}1} as follows a_n\equal{}0, if number of positive divisors of

n

is odd a_n\equal{}1, if number of positive divisors of

n

is even (The positive divisors of

n

include

1

as well as

n

.)Let x\equal{}0.a_1a_2a_3........ be the real number whose decimal expansion contains

a_n

in the

n

-th place,

n\geq1

.Determine,with proof,whether

x

is rational or irrational.

2