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%I #39 Sep 08 2022 08:46:05
%S 0,1,2,3,4,5,6,7,8,9,12,24,36,48,75,81,100,121,144,147,150,169,192,
%T 196,200,225,242,288,300,320,324,363,375,400,441,484,500,507,512,529,
%U 600,640,648,700,704,735,800,832,882,900,960,961,1014,1083,1088,1200,1250,1452,1458,1521,1681,1815
%N Numbers n such that n*(sum of digits of n) is a perfect square.
%e 375*(3+7+5) = 5625 = 75^2. So, 375 is a member of this sequence.
%t Select[Range[0, 1815], IntegerQ@ Sqrt[# Plus @@ IntegerDigits@ #] &] (* _Michael De Vlieger_, Apr 12 2015 *)
%o (Python)
%o def DS(n):
%o s = 0
%o for i in str(n):
%o s += int(i)
%o return s
%o for n in range(10**3):
%o k = 0
%o while k**2 <= n*DS(n):
%o if k**2 == n*DS(n):
%o print(n,end=', ')
%o break
%o else:
%o k += 1
%o # Edited by _Derek Orr_ Apr 10 2015
%o (Magma) [n: n in [0..1000] | IsSquare(n*(&+Intseq(n)))]; // _Vincenzo Librandi_, Sep 20 2013
%o (PARI) for(n=0,2000,s=sumdigits(n);if(issquare(n*s),print1(n,", "))) \\ _Derek Orr_, Apr 10 2015
%o (Sage) [x for x in [0..2000] if is_square(x*sum(Integer(x).digits(base=10)))] # _Bruno Berselli_, May 25 2015
%Y Cf. A007953.
%K nonn,base,easy
%O 1,3
%A _Derek Orr_, Sep 19 2013
%E More terms from _Derek Orr_, Apr 10 2015
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