A218013 Numbers that divide the product of the nonzero digits (in base 10) of their square.
1, 2, 3, 5, 6, 8, 28, 36, 42, 54, 75, 192, 216, 288, 486, 525, 648, 768, 864, 882, 1728, 2160, 3024, 6048, 6075, 7056, 7680, 17280, 18144, 20736, 30240, 40824, 56448, 60480, 61236, 62208, 64512, 84672, 122472, 138915, 150528, 387072, 408240, 497664, 622080
Offset: 1
Examples
For n=5, n^2 is 25; the product of the digits of 25 is 2 * 5 = 10, which is divisible by n=5.
Links
- David A. Corneth, Table of n, a(n) for n = 1..10919 (first 473 terms from Chai Wah Wu; terms <= 10^100)
Programs
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PARI
isok(n) = digs = digits(n^2); (prod(i=1, #digs, if (digs[i], digs[i], 1)) % n) == 0; \\ Michel Marcus, Aug 12 2013
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Python
from operator import mul from functools import reduce from gmpy2 import t_mod, mpz A218013 = [n for n in range(1,10**6) if not t_mod(reduce(mul,(mpz(d) for d in str(n**2) if d != '0')),n)] # Chai Wah Wu, Aug 23 2014