Katagiri calls a number nude if it is divisible by each of its digits e.g like 672.
Clearly this definition (there exist other as well!) implies non-zero numbers only.

a. How many nude numbers are there below 1,000,000?
b. Evaluate the smallest nude number which contains all the odd digits.
c. Find the smallest triplet of consecutive nontrivial nude numbers.
d. Prove that there is infinite number of nude numbers.