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

1,2

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).

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A061460 A016935 A241756 * A128794 A195804 A145259

Adjacent sequences: A236217 A236218 A236219 * A236221 A236222 A236223

Keyword

base,nonn

Author

K. D. Bajpai, Jan 20 2014

Status

approved