A144261: a(n) = smallest k such that k*n is a Niven (or Harshad) number.

harshad.py

# A Harshad number (or Niven number) is a number that is divisible by its sum of digits.

def sum_of_digits(n):
    s = 0
    while n > 0:
        s += (n % 10)
        n /= 10
    return s
# Alternative one-liner:
# sum_of_digits = lambda n: sum(map(int, str(n)))

# Note: will raise an error if n == 0.
def harshad(n):
    return n % sum_of_digits(n) == 0

first100terms = [1,1,1,1,1,1,1,1,1,1,10,1,9,3,2,3,6,1,6,1,1,5,9,1,2,6,
                 1,3,9,1,12,6,4,3,2,1,3,3,3,1,10,1,12,3,1,5,9,1,8,1,2,
                 3,18,1,2,2,2,9,9,1,12,6,1,3,3,2,3,3,3,1,18,1,7,3,2,2,
                 4,2,9,1,1,5,18,1,6,6,3,3,9,1,4,5,4,9,2,2,12,4,2,1]
print "# A144261"
for n in xrange(1, 10001):
    k = 1
    while not harshad(k * n):
        k += 1
    print n, k
    if n <= 100:
        assert k == first100terms[n-1]