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

1, 8, 512, 4913, 5832, 17576, 19683, 64000, 125000, 314432, 421875, 1000000, 1124864, 1259712, 1404928, 3176523, 8000000, 91125000, 130323843, 191102976, 274625000, 348913664, 512000000, 791453125

Offset: 1

Author

K. D. Bajpai, Jan 20 2014

Keywords

• base
• nonn

Comments

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).

Examples

			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.
		

Links

• K. D. Bajpai and Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 110 terms from K. D. Bajpai)

Crossrefs

Cf. A000290 (squares), A007953 (digital sum), A061209.

Programs

Maple

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);

Mathematica

Select[Range[10^4]^3, IntegerQ@ Sqrt[#/Total[ IntegerDigits@#]] &] (* Giovanni Resta, Jan 20 2014 *)

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