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Numbers k that have at least two different representations as the product of a number and of its decimal digits.
6

%I #32 Aug 13 2020 10:11:13

%S 0,192,648,819,1197,1536,4872,4977,5976,7056,9968,13608,20448,21168,

%T 22176,22428,22752,32040,33984,35424,36864,37692,38736,59778,64152,

%U 77600,89928,96912,112833,112896,113148,116352,116736,120384,120708,146412,154752,156288,192888

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

%C Subsequence of A336826.

%H Chai Wah Wu, <a href="/A336944/b336944.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..500 from Seiichi Manyama)

%e 192 = 24 * (2*4) = 32 * (3*2).

%e 549504 = 1696 * (1*6*9*6) = 2862 * (2*8*6*2) = 3392 * (3*3*9*2) = 3816 * (3*8*1*6).

%e 1798848 = 6246 * (6*2*4*6) = 12492 * (1*2*4*9*2) = 33312 * (3*3*3*1*2).

%t 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 *)

%Y Cf. A098736, A336826, A336876.

%K nonn,base

%O 1,2

%A _Seiichi Manyama_, Aug 08 2020