A175396 Numbers whose sum of squares of digits is a square.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 34, 40, 43, 50, 60, 68, 70, 80, 86, 90, 100, 122, 148, 184, 200, 212, 221, 236, 244, 263, 269, 296, 300, 304, 326, 340, 362, 366, 400, 403, 418, 424, 430, 442, 447, 474, 481, 488, 500, 600, 608, 623, 629, 632, 636, 663

Offset: 1

Author

Ctibor O. Zizka, Apr 30 2010

Keywords

• base
• easy
• nonn

Comments

Previous name: Numbers n such that Sum_{i=1..r, x(i)^2} is a perfect square, where x(i) = digits of n. r=1+floor(log_10 n).

Examples

			34 is a term: 3^2 + 4^2 = 25 = 5^2.
122 is a term: 1^2 + 2^2 + 2^2 = 9 = 3^2.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A003132, A084561.

Programs

Mathematica

Select[Range[0, 666], IntegerQ[Sqrt[Plus @@ (IntegerDigits[#]^2)]] &] (* Ivan Neretin, Aug 03 2015 *)

PARI

isok(n) = {my(digs = digits(n)); issquare(sum(i=1, #digs, digs[i]^2))} \\ Michel Marcus, Jun 02 2013

Python

from math import isqrt
def ok(n): s = sum(int(i)**2 for i in str(n)); return isqrt(s)**2 == s
print(*[k for k in range(664) if ok(k)], sep = ', ')  # Ya-Ping Lu, Jul 07 2025

Extensions

Corrected and extended by Neven Juric, Jul 12 2010

Simpler definition by Michel Marcus, Jun 02 2013