%I #29 Sep 08 2022 08:44:28

%S 1,2,3,4,5,6,7,8,9,12,24,36,48,81,100,144,150,192,200,225,288,300,320,

%T 324,375,400,441,500,512,600,640,648,700,704,735,800,832,882,900,960,

%U 1014,1088,1200,1452,1458,1521,1815,2023

%N Numbers k such that k / (sum of digits of k) is a square.

%C The sequence is infinite since if m = 10^(2*j) then m / digitsum(m) = m. - _Marius A. Burtea_, Dec 21 2018

%H Reinhard Zumkeller, <a href="/A001102/b001102.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) mod A007953(a(n)) = 0 and A010052(a(n) / A007953(a(n))) = 1. - _Reinhard Zumkeller_, Aug 17 2011

%t Select[Range[2200],IntegerQ[Sqrt[#/Total[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Feb 25 2012 *)

%o (Haskell)

%o a001102 n = a001102_list !! (n-1)

%o a001102_list =

%o filter (\x -> a010052 (x `div` (a007953 x)) == 1) a005349_list

%o -- _Reinhard Zumkeller_, Aug 17 2011

%o (Magma) [n: n in [1..1000] | IsIntegral(n/(&+Intseq(n))) and IsSquare(n/(&+Intseq(n)))]; // _Marius A. Burtea_, Dec 21 2018

%Y Subsequence of Niven numbers (A005349); cf. A028839.

%K nonn,base,nice

%O 1,2

%A _N. J. A. Sloane_, Bill Moran (moran1(AT)llnl.gov)