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Numbers n in which the last K digits of n form an integer divisible by K^2, for K = 1, 2, ..., M, where M is the number of digits in n.
4

%I #5 Nov 21 2013 12:47:57

%S 1,2,3,4,5,6,7,8,9,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,

%T 80,84,88,92,96,108,144,180,216,252,288,324,360,396,432,468,504,540,

%U 576,612,648,684,720,756,792,828,864,900,936,972,1072,1216,1360,1504,1648

%N Numbers n in which the last K digits of n form an integer divisible by K^2, for K = 1, 2, ..., M, where M is the number of digits in n.

%C The terms satisfying the definition become increasingly rare as the number of their digits increases. There are only 214 such terms up to 1 million, the last of which is 990000. [From Harvey P. Dale, Apr 10 2012]

%H Harvey P. Dale, <a href="/A079238/b079238.txt">Table of n, a(n) for n = 1..200</a>

%e a(84)=4864 because 4 is divisible by 1^2, 64 by 2^2, 864 by 3^2, 4864 by 4^2.

%t idkQ[n_]:=Module[{idn=IntegerDigits[n]},And@@Table[Divisible[ FromDigits[ Take[idn,-i]],i^2],{i,Length[idn]}]]; Select[Range[1700],idkQ] (* _Harvey P. Dale_, Apr 10 2012 *)

%K base,nonn

%O 1,2

%A Sudipta Das (juitech(AT)vsnl.net), Feb 03 2003