A246337 Numbers n which when expressed in base 16 are palindromes whose digit sum and digit product both divide n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 273, 69905, 78129, 200979, 17903889, 4581298449, 1172816597265, 1174959919377, 300240008712465, 300240176484625, 370608786444625

Offset: 1

Author

Chai Wah Wu, Aug 22 2014

Keywords

• nonn
• base

Crossrefs

Cf. A117228, A246338.

Programs

Python

from operator import mul
from functools import reduce
from gmpy2 import t_mod, digits, mpz
A246337 = sorted([mpz(n,16) for n in (digits(x,16)+digits(x,16)[::-1]
    for x in range(1,16**7)) if not (n.count('0') or
    t_mod(mpz(n,16), sum((mpz(d,16) for d in n)))
    or t_mod(mpz(n,16), reduce(mul,(mpz(d,16) for d in n))))] +
    [mpz(n,16) for n in (digits(x,16)+digits(x,16)[-2::-1]
    for x in range(16**7)) if not (n.count('0') or
    t_mod(mpz(n,16), sum((mpz(d,16) for d in n)))
    or t_mod(mpz(n,16), reduce(mul,(mpz(d,16) for d in n))))])