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A236220 Cubes which when divided by their digital sum, become square.

%I A236220 #18 Jan 29 2014 05:54:55
%S A236220 1,8,512,4913,5832,17576,19683,64000,125000,314432,421875,1000000,
%T A236220 1124864,1259712,1404928,3176523,8000000,91125000,130323843,191102976,
%U A236220 274625000,348913664,512000000,791453125
%N A236220 Cubes which when divided by their digital sum, become square.
%C A236220 The term digital sum represents: sum of the digits of a number e.g. the digital sum of 4913 is (4+9+1+3 = 17).
%H A236220 K. D. Bajpai and Giovanni Resta, <a href="/A236220/b236220.txt">Table of n, a(n) for n = 1..1000</a> (first 110 terms from K. D. Bajpai)
%e A236220 19683 is in the sequence because 19683 divided by its digital sum (1+9+6+8+3 = 27) gives 729 which is a square: 729 = 27^2.
%e A236220 314432 is in the sequence because 314432 divided by its digital sum (3+1+4+4+3+2 = 17) gives 18496 which is a square: 18496 = 136^2.
%p A236220 with(StringTools):KD := proc() local a,b,d,e; a:=n^3; b:=add( i,i = convert((a), base,10))(a); d:=a/b; if d=floor(d) then e:=evalf(d^(1/2)); if e=floor(e)then RETURN (a);fi;fi; end: seq(KD(), n=1..3000);
%t A236220 Select[Range[10^4]^3, IntegerQ@ Sqrt[#/Total[ IntegerDigits@#]] &] (* _Giovanni Resta_, Jan 20 2014 *)
%o A236220 (PARI)
%o A236220 i2d(x) = if(x==0, return([0])); v=[]; while(x>0, y=x%10; x\=10; v=concat(y, v)); v
%o A236220 digsum(n) = d=i2d(n); sum(i=1, #d, d[i])
%o A236220 s=[]; for(n=1, 1000, c=n^3; if(issquare(c/digsum(c)), s=concat(s, c))); s \\ _Colin Barker_, Jan 20 2014
%Y A236220 Cf. A000290 (squares), A007953 (digital sum), A061209.
%K A236220 base,nonn
%O A236220 1,2
%A A236220 _K. D. Bajpai_, Jan 20 2014