A379984 Numbers that are divisible by the square of the product of their digits.

1, 11, 12, 111, 112, 1111, 1112, 1116, 2112, 11111, 11112, 11172, 11232, 11711, 12112, 21312, 32112, 111111, 111112, 111132, 111312, 112112, 113112, 114112, 122112, 131112, 218112, 311112, 1111111, 1111112, 1111113, 1111131, 1111311, 1111712, 1112112, 1113111

Offset

1,2

Comments

Called "Second-order Zuckerman numbers" by Pal (2024).

Links

Amiram Eldar, Table of n, a(n) for n = 1..111

Pradip Kumar Pal, Second Order Zuckerman Number, International Journal of Mathematical Education, Vol. 14, No. 1 (2024), pp. 1-3.

Mathematica

Select[Range[10^5], FreeQ[d = IntegerDigits[#], 0] && Divisible[#, (Times @@ d)^2] &]

Prog

(PARI) isok(k) = my(m = vecprod(digits(k))); m > 0 && !(k % m^2);

Crossrefs

Subsequence of A007602.

Sequence in context: A096299 A110382 A095764 * A342944 A363931 A296447

Adjacent sequences: A379981 A379982 A379983 * A379985 A379986 A379987

Keyword

nonn,base

Author

Amiram Eldar, Jan 07 2025

Status

approved