An integer n is called 'paladin' if the number of positive divisors of n is equal to the number of digits of n.

a) Determine all three-digit 'paladin' numbers.

b) Determine a 'paladin' number with four digits that is less than 1300.

[OPM 2012 Level Beta Paper1 Q2][Original in Portuguese. My translation into English.]

[OPM = Olimpiada Paulista de Matematica, Brazil]

The same question is repeated in the Gamma Level paper (borderline middle/upper secondary) but with a harder part (b).

b2) Determine a 'paladin' number with six digits that is less than 110000.

[OPM 2012 Level Gamma Paper 1 Q1]

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