A066156 a(n) is the least k>n such that k*n = (product of digits of k) * (sum of digits of k), or 0 if no such k exists.

10, 135, 15, 139968, 18, 756, 476, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Robert G. Wilson v, Dec 13 2001

Keywords

• base
• nonn

Comments

a(n) = 0 for all n > 8: see A049101. - Robert Israel, Aug 18 2020

Crossrefs

Cf. A007953 (sum of digits), A007954 (product of digits).

Cf. A049101.

Programs

Mathematica

Do[ k = n + 1; While[ k*n != Apply[Times, IntegerDigits[k]] Apply[Plus, IntegerDigits[k]], k++ ]; Print[k], {n, 0, 10} ]

Extensions

Edited by Robert Israel, Aug 18 2020