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

0, 1, 36, 81, 100, 144, 289, 441, 784, 900, 1225, 1296, 3025, 3600, 5041, 5625, 6400, 8100, 8649, 10000, 11881, 15625, 15876, 18225, 23716, 36100, 41616, 44100, 50625, 55225, 57600, 62001, 67600, 72900, 78400, 99225, 122500, 129600, 136900, 145161, 168921, 189225

Offset: 1

Author

Paolo P. Lava, Apr 11 2016

Keywords

• nonn
• easy
• base

Examples

			0 = 0^2; 1 = 1^2; 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A037123, A271626.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,k,n; a:=0; for n from 0 to q do b:=0; c:=n;
for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
if a=trunc(sqrt(a))*trunc(sqrt(a)) then print(a); fi; od; end: P(10^6);

Mathematica

Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 10^4]], IntegerQ@ Sqrt@ # &] (* Michael De Vlieger, Apr 11 2016 *)

PARI

lista(nn) = for (n=0, nn, if (issquare(s=sum(k=1, n, sumdigits(k))), print1(s, ", "))); \\ Michel Marcus, Apr 11 2016