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

%I A236077 #20 Jan 22 2014 20:26:16
%S A236077 1,8,512,1000,8000,19683,35937,46656,59319,74088,125000,157464,185193,
%T A236077 328509,373248,421875,474552,512000,592704,658503,804357,1000000,
%U A236077 1157625,1259712,1331000,1367631,1481544,2460375,2628072
%N A236077 Cubes which remain (integer) cubes when divided by their digital sum.
%H A236077 Charles R Greathouse IV, <a href="/A236077/b236077.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Bajpai)
%e A236077 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.
%e A236077 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.
%p A236077 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);
%o A236077 (PARI)
%o A236077 digsum(n) = d=eval(Vec(Str(n))); sum(i=1, #d, d[i])
%o A236077 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
%Y A236077 Intersection of A005349 and A053058.
%Y A236077 Cf. A000578 (cubes), A007953 (digital sum).
%K A236077 base,nonn
%O A236077 1,2
%A A236077 _K. D. Bajpai_, Jan 19 2014