J (9)
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Assumes the value to be tested is in variable `b` <s>(I know this can be made into a function, but don't have a clue on *how*. J is confusing. Any help on this is appreciated)</s> Thanks Marinus!

    (-:~.)@":

Checks if the lenght of the string rep of the number with all the duplicates removed is the same as the lenght of the regular string rep.