A236077 Cubes which remain (integer) cubes when divided by their digital sum.

1, 8, 512, 1000, 8000, 19683, 35937, 46656, 59319, 74088, 125000, 157464, 185193, 328509, 373248, 421875, 474552, 512000, 592704, 658503, 804357, 1000000, 1157625, 1259712, 1331000, 1367631, 1481544, 2460375, 2628072

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 100 terms from Bajpai)

Example

19683 is in the sequence because 19683 divided by its digital sum (1+9+6+8+3 = 27) gives 729 which is also a cube: 729 = 9^3.
46656 is in the sequence because 46656 divided by its digital sum (4+6+6+5+6 = 27) gives 1728 which is also a cube: 1728 = 12^3.

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; e:=evalf(d^(1/3));  if e=floor(e) then RETURN (a); fi;  end: seq(KD(), n=1..200);

Prog

(PARI)
digsum(n) = d=eval(Vec(Str(n))); sum(i=1, #d, d[i])
s=[]; for(n=1, 200, d=digsum(n^3); if(n^3%d==0 && ispower(n^3\d, 3), s=concat(s, n^3))); s \\ Colin Barker, Jan 22 2014

Crossrefs

Intersection of A005349 and A053058.

Cf. A000578 (cubes), A007953 (digital sum).

Sequence in context: A281136 A228292 A082385 * A061460 A016935 A241756

Adjacent sequences: A236074 A236075 A236076 * A236078 A236079 A236080

Keyword

base,nonn

Author

K. D. Bajpai, Jan 19 2014

Status

approved