A336944 Numbers k that have at least two different representations as the product of a number and of its decimal digits.

0, 192, 648, 819, 1197, 1536, 4872, 4977, 5976, 7056, 9968, 13608, 20448, 21168, 22176, 22428, 22752, 32040, 33984, 35424, 36864, 37692, 38736, 59778, 64152, 77600, 89928, 96912, 112833, 112896, 113148, 116352, 116736, 120384, 120708, 146412, 154752, 156288, 192888

Offset: 1

Author

Seiichi Manyama, Aug 08 2020

Keywords

• nonn
• base

Comments

Subsequence of A336826.

Examples

			192 = 24 * (2*4) = 32 * (3*2).
549504 = 1696 * (1*6*9*6) = 2862 * (2*8*6*2) = 3392 * (3*3*9*2) = 3816 * (3*8*1*6).
1798848 = 6246 * (6*2*4*6) = 12492 * (1*2*4*9*2) = 33312 * (3*3*3*1*2).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..500 from Seiichi Manyama)

Crossrefs

Cf. A098736, A336826, A336876.

Programs

Mathematica

digprod[n_] := n * Times @@ IntegerDigits[n]; seqQ[0] = True; seqQ[n_] := DivisorSum[n, Boole[digprod[#] == n] &] > 1; Select[Range[0, 2 * 10^5], seqQ] (* Amiram Eldar, Aug 08 2020 *)
Take[Select[Tally[Table[n*Times@@IntegerDigits[n],{n,30000}]],#[[2]]>1&][[;;,1]]//Sort,40] (* Harvey P. Dale, Apr 13 2025 *)