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A236220
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Cubes which when divided by their digital sum, become square.
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1
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1, 8, 512, 4913, 5832, 17576, 19683, 64000, 125000, 314432, 421875, 1000000, 1124864, 1259712, 1404928, 3176523, 8000000, 91125000, 130323843, 191102976, 274625000, 348913664, 512000000, 791453125
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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.
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MAPLE
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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);
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MATHEMATICA
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Select[Range[10^4]^3, IntegerQ@ Sqrt[#/Total[ IntegerDigits@#]] &] (* Giovanni Resta, Jan 20 2014 *)
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PROG
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(PARI)
i2d(x) = if(x==0, return([0])); v=[]; while(x>0, y=x%10; x\=10; v=concat(y, v)); v
digsum(n) = d=i2d(n); sum(i=1, #d, d[i])
s=[]; for(n=1, 1000, c=n^3; if(issquare(c/digsum(c)), s=concat(s, c))); s \\ Colin Barker, Jan 20 2014
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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