A395129 Numbers k that are the concatenation of three distinct divisors of k.

124, 126, 128, 132, 135, 162, 168, 175, 184, 216, 248, 264, 312, 315, 324, 384, 396, 412, 432, 612, 624, 648, 672, 728, 735, 784, 816, 824, 864, 936, 1128, 1155, 1168, 1173, 1197, 1210, 1212, 1216, 1220, 1224, 1230, 1236, 1240, 1248, 1250, 1260, 1280, 1288, 1296, 1320, 1326, 1350, 1365, 1368

Offset

1,1

Comments

Leading zeros are not allowed.

If k is a term, then so are 10^m*k for m > 0, with at most two exceptions.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 135 is a term because it is the concatenation of 1, 3 and 5, which are all distinct and all divide 135.

Maple

filter:= proc(n) local i, j, a, bc, b, c;
   for i from 1 to ilog10(n)-1 do
     a:= n mod 10^i;
     if a < 10^(i-1) or n mod a <> 0 then next fi;
     bc:= (n-a)/10^i;
     for j from 1 to ilog10(bc) do
       c:= bc mod 10^j;
       if c = a or c < 10^(j-1) or n mod c <> 0 then next fi;
       b:= (bc-c)/10^j;
       if b <> a and b <> c and n mod b = 0 then return true fi;
   od od;
   false
end proc:
select(filter, [$1..10^4]);

Mathematica

f[{a_, b_, c_}]:=FromDigits[Flatten[IntegerDigits/@{a, b, c}]]; q[k_]:=ContainsAny[f/@Permutations[Drop[Divisors[k], -1], {3}], {k}]; Select[Range[1368], q] (* James C. McMahon, Apr 17 2026 *)

Crossrefs

Cf. A392961.

Sequence in context: A214464 A288353 A080537 * A030492 A031203 A107221

Adjacent sequences: A395126 A395127 A395128 * A395130 A395131 A395132

Keyword

nonn,base

Author

Robert Israel, Apr 12 2026

Status

approved