%I #19 Jan 14 2021 21:16:40
%S 9,96,963,9632,96325,963252,6480005
%N The largest n-digit number whose first k digits are divisible by k^2 for k = 1..n.
%C There are 7 terms in the sequence and the 7-digit number 6480005 is the largest number to satisfy the requirements.
%e There are nine one-digit numbers divisible by 1 and the largest is 9, so a(1)=9.
%e For two-digit numbers, the second digit must make it divisible by 2^2, which gives 96 as the largest to satisfy the requirement, so a(2)=96.
%t a = Table[j, {j, 9}]; r = 2; t = {}; While[! a == {}, n = Length[a]; nmax = Last[a]; k = 1; b = {}; While[! k > n, z0 = a[[k]]; Do[z = 10*z0 + j; If[Mod[z, r*r] == 0, b = Append[b, z]], {j, 0, 9}]; k++]; AppendTo[t, nmax]; a = b; r++]; t
%Y Cf. A079042.
%K nonn,base,fini,full
%O 1,1
%A _Shyam Sunder Gupta_, Aug 08 2013