This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A147553 #15 Jul 16 2021 03:24:55
%S A147553 1,143,142857143,142857142857143,142857142857142857143,
%T A147553 142857142857142857142857143,142857142857142857142857142857143,
%U A147553 142857142857142857142857142857142857143
%N A147553 Numbers k such that k^2 divides k.k where dot "." means concatenation.
%C A147553 I proved that for n > 0, a(n+1) = (10^(6n-3) + 1)/7. Namely for n > 1, a(n) is of the form 142857.142857. ... .142857.143. Except for a(1), 11 divides all terms, so there is no prime p such that p^2 divides p.p. For n > 1, a(n).a(n)/(a(n)*a(n))=7.
%H A147553 Robert Israel, <a href="/A147553/b147553.txt">Table of n, a(n) for n = 1..167</a>
%H A147553 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1000001,-1000000).
%e A147553 143*143|143.143 (143143/(143*143)=7) so 143 is in the sequence.
%p A147553 1, seq((10^(6*n-3)+1)/7, n=1..20); # _Robert Israel_, Sep 26 2016
%t A147553 a[0]=1;a[n_]:=(10^(6n-3)+1)/7;Table[a[k],{k,0,8}]
%t A147553 Do[d=Divisors[10^i+1];s=Select[d,Length[IntegerDigits[#]]==i&];If[Length[s]>0,Do[Print[s[[j]]],{j,Length[s]}]],{i,69}] (* _Hans Havermann_, May 31 2014 *)
%t A147553 LinearRecurrence[{1000001,-1000000},{1,143,142857143},20] (* _Harvey P. Dale_, Apr 02 2018 *)
%Y A147553 Cf. A147554, A243162 (k^2 divides k.k.k).
%K A147553 base,easy,nice,nonn
%O A147553 1,2
%A A147553 _Farideh Firoozbakht_, Dec 23 2008