%I #39 Mar 09 2024 11:05:40

%S 1,2,3,6,9,10,11,12,13,14,15,18,20,21,22,23,30,31,39,41,45,48,51,58,

%T 59,60,67,68,76,77,85,86,90,94,95,100,101,102,103,104,105,110,111,112,

%U 113,120,121,122,130,131,139,140,148,150,157,158,166,175,176,180,184,185

%N Positive numbers k such that sum of digits of k^2 is a square.

%H Bruno Berselli, <a href="/A061910/b061910.txt">Table of n, a(n) for n = 1..1000</a>

%H MathStackExchange, <a href="https://math.stackexchange.com/questions/1093266/numbers-n-such-that-the-digit-sum-of-n2-is-a-square/2258657">Numbers n such that the digit sum of n2 is a square</a>, 2015-2016.

%e 6^2 = 36 and 3+6 = 9 is a square. 13^2 = 169 and 1+6+9 = 16 is a square.

%p readlib(issqr): f := []: for n from 1 to 200 do if issqr(convert(convert(n^2,base,10),`+`)) then f := [op(f), n] fi; od; f;

%t Select[Range[185], IntegerQ[Sqrt[Total[IntegerDigits[#^2]]]] &] (* _Jayanta Basu_, May 06 2013 *)

%o (Magma) [ n: n in [1..185] | IsSquare(&+Intseq(n^2)) ]; // _Bruno Berselli_, Jul 29 2011

%o (PARI) is(n)=n=eval(Vec(Str(n^2)));issquare(sum(i=1,#n,n[i])) \\ _Charles R Greathouse IV_, Jul 29 2011

%o (PARI) select( is_A061910(n)=issquare(sumdigits(n^2)), [0..199]) \\ Includes the initial 0. - _M. F. Hasler_, Oct 16 2017

%o (Python)

%o from gmpy2 import is_square

%o A061910 = [n for n in range(1,10**3) if is_square(sum(int(d) for d in str(n*n)))] # _Chai Wah Wu_, Sep 03 2014

%Y Cf. A007953, A004159, A053057, A061909, A061911, A061912.

%Y Sequence A293832 gives the start of the first run of n consecutive values.

%K nonn,base

%O 1,2

%A _Asher Auel_, May 17 2001