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

editing

approved

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]

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

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

approved

editing

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 .

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

base,nonn,new

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 .

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, 80, 84, 88, 92, 96, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1072, 1216, 1360, 1504, 1648

1,2

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

base,nonn

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

approved