A287442 Numbers k = concat( x, y ), not ending in 0, such that x * y divides k.

11, 12, 15, 24, 36, 101, 102, 104, 105, 125, 208, 306, 315, 735, 1001, 1002, 1004, 1005, 1008, 1025, 1125, 1352, 1734, 2016, 3006, 3015, 3024, 3375, 6048, 7007, 7056, 9072, 10001, 10002, 10004, 10005, 10008, 10016, 10025, 10125, 10625, 11011, 13013, 14112, 18144

Offset

1,1

Comments

Numbers ending in zero are not listed because of the form a(n) * 10^k, with k>0.

Links

Table of n, a(n) for n=1..45.

Paolo P. Lava, First 250 terms with their ratios

Example

36 = concat(3,6) and 36 / (3*6) = 2;
3375 = concat(3,375) and 3375 / (3*375) = 3;
18144 = concat(18,144) and 18144 / (18*144) = 7.

Maple

P:=proc(q) local a, k, n; for n from 1 to q do if not n mod 10=0 then
for k from 1 to ilog10(n) do a:=n/((n mod 10^k)*trunc(n/10^k));
if type(a, integer) then print(n); break; fi; od; fi; od; end: P(10^9);

Mathematica

cxyQ[n_]:=Module[{idn=IntegerDigits[n]}, idn[[-1]]!=0&&AnyTrue[ Table[ FromDigits/@TakeDrop[idn, k], {k, Length[idn]-1}], Divisible[n, Times@@#]&]]; Select[Range[20000], cxyQ] (* The program uses the AnyTrue function from Mathematica version 10 *)(* Harvey P. Dale, Mar 09 2018 *)

Crossrefs

Sequence in context: A249766 A113600 A255725 * A255726 A347541 A097158

Adjacent sequences: A287439 A287440 A287441 * A287443 A287444 A287445

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 25 2017

Status

approved