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Numbers n such that the square root of n is an integer and a multiple of the sum of the digits of n.
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%I #26 Feb 19 2020 08:53:47

%S 1,81,100,324,400,1296,2025,2401,2704,2916,4225,5184,6400,7744,8100,

%T 10000,11664,12544,20736,26244,32400,33124,36100,39204,40000,46656,

%U 59049,63504,72900,75625,88209,104329,104976,122500,123201,129600

%N Numbers n such that the square root of n is an integer and a multiple of the sum of the digits of n.

%H Mehrad Mahmoudian, <a href="/A067521/b067521.txt">Table of n, a(n) for n = 1..10000</a>

%H Mehrad Mahmoudian, <a href="https://gitlab.com/m.mahmoudian/coding-oeis/-/blob/master/A067521/A067521.R">R code to produce the sequence</a>

%e 18^2=324, 18=2*(3+2+4), so 324 is in the sequence.

%p dig := X->convert((convert(X,base,10)),`+`); seq(`if`(isprime(i)=false,`if`(i mod dig(i^2)=0,i^2,NULL),NULL),i=1..1000);

%t Select[Range[500]^2,Divisible[Sqrt[#],Total[IntegerDigits[#]]]&] (* _Harvey P. Dale_, Jul 15 2013 *)

%Y Subsequence of squares (A000290).

%Y Cf. A067520 (similar for triangular numbers).

%K base,easy,nonn

%O 1,2

%A _Amarnath Murthy_, Feb 14 2002

%E More terms from _Sascha Kurz_ and Francois Jooste (phukraut(AT)hotmail.com), Mar 18 2002

%E Definition corrected by _Harvey P. Dale_, Jul 15 2013