The program below reports that 432 is the smallest positive integer whose factorial is not divisble by the sum of its digits.
# Find the smallest positive integer, n, for which n! is *not* divisible
# by the sum of its digits.
def sum_digits(n):
""" Return the sum of the decimal digits of n. """
s = 0
while n:
s += n % 10
n //= 10
return s
n = nfac = 1
while True:
nfac *= n
digit_sum = sum_digits(nfac)
if nfac % digit_sum:
# Success! report and exit the loop
print('{}! is not divisible by the sum of its digits'.format(n))
break
n += 1