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Y.Katagiri calls a number nude if it is divisible by all of its digits (which should be nonzero) like  . (The number is called "nude" because it exposes some of its factors).

There are only 9039 such numbers below one million, however there are infinite nude numbers since all repdigits are nude.

The smallest nude number which contains all the odd digits is 1117935. Note that if a nude number contains a `5', then all the other digits must be odd.

The smallest nude    which contains the maximal (8) number of distinct digits is 1123449768. The smallest triple of consecutive nontrivial nude numbers is (1111, 1112, 1113). It is easy to see that there cannot be 4 consecutive nude numbers greater than 10.

The smallest 3 × 3 magic square whose entries are nontrivial consecutive nude numbers is

 883416 883128 883344 883224 883296 883368 883248 883464 883176

The first nude numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 111, 112, 115, 122, 124, 126, 128 more terms

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