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A271629 Squares that are the sum of the digits of the numbers from 0 to n, for some n.

%I A271629 #14 Apr 11 2016 23:26:37
%S A271629 0,1,36,81,100,144,289,441,784,900,1225,1296,3025,3600,5041,5625,6400,
%T A271629 8100,8649,10000,11881,15625,15876,18225,23716,36100,41616,44100,
%U A271629 50625,55225,57600,62001,67600,72900,78400,99225,122500,129600,136900,145161,168921,189225
%N A271629 Squares that are the sum of the digits of the numbers from 0 to n, for some n.
%H A271629 Paolo P. Lava, <a href="/A271629/b271629.txt">Table of n, a(n) for n = 1..1000</a>
%e A271629 0 = 0^2; 1 = 1^2; 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2.
%p A271629 with(numtheory): P:=proc(q) local a,b,c,k,n; a:=0; for n from 0 to q do b:=0; c:=n;
%p A271629 for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
%p A271629 if a=trunc(sqrt(a))*trunc(sqrt(a)) then print(a); fi; od; end: P(10^6);
%t A271629 Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 10^4]], IntegerQ@ Sqrt@ # &] (* _Michael De Vlieger_, Apr 11 2016 *)
%o A271629 (PARI) lista(nn) = for (n=0, nn, if (issquare(s=sum(k=1, n, sumdigits(k))), print1(s, ", "))); \\ _Michel Marcus_, Apr 11 2016
%Y A271629 Cf. A037123, A271626.
%K A271629 nonn,easy,base
%O A271629 1,3
%A A271629 _Paolo P. Lava_, Apr 11 2016