Is every factorial divisible by its sum of digits?
Solution 1:
It's not true. The first counterexample is for $ n = 432 $. The sum of the digits in $ 432! $ is 3897, which you can see using Wolfram Alpha. But the prime factorisation of 3897 is $ 3^2 \times 433 $, so $ 432! $ cannot be divisible by its sum of digits.
The list of counterexamples is sequence A066419 in the OEIS.