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

Author

K. D. Bajpai, Jan 19 2014

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Intersection of A005349 and A053058.

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

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

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