A053058 -id:A053058 - cp's OEIS frontend

A237525 Numbers k such that the sum of digits of k^3 is a cube.

0, 1, 2, 5, 8, 10, 11, 20, 27, 33, 36, 39, 42, 50, 54, 57, 69, 72, 75, 78, 80, 84, 87, 93, 100, 101, 105, 108, 110, 111, 114, 135, 138, 147, 162, 165, 168, 174, 177, 200, 219, 222, 225, 228, 231, 234, 258, 267, 270, 273, 276, 285, 291, 294, 312

Offset: 1

Derek Orr, Feb 09 2014

If k is in the sequence then so is 10*k. - David A. Corneth, May 26 2021

			36^3 = 46656. DigitSum(46656) = 27 (also a cube). So, 36 is a member of this sequence.

David A. Corneth, Table of n, a(n) for n = 1..10866

Cf. A061910, A007953, A004164, A053058.

isok(n) = ispower(sumdigits(n^3), 3); \\ Michel Marcus, Feb 09 2014

a(n) = A053058(n)^(1/3).

A371004 Fourth powers whose digital sum is also a fourth power.

Original entry on oeis.org

0, 1, 10000, 14641, 100000000, 104060401, 146410000, 1000000000000, 1004006004001, 1040604010000, 1464100000000, 4228599998736, 8670998958336, 9748688599521, 9948826238976, 12598637895936, 19226786746896, 19896452775936, 20699669996721, 23768199069696, 26599197668481

Offset: 1

Stefano Spezia, Mar 08 2024

Among the terms of this sequence, there are:
  the numbers of the form 10^(4*k) with k >= 0;
  the numbers of the form (10^i + 10^j)^4 with i > j >= 0.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A000583, A007953, A038444, A053057, A053058, A371047.

Select[Range[0,2500]^4, IntegerQ[DigitSum[#]^(1/4)]&]

a(n) = A371047(n)^4.

A180738 Largest n-digit cube whose sum of digits is also a cube, or 0 if there is no such number.

Original entry on oeis.org

8, 0, 512, 8000, 74088, 804357, 8000000, 74088000, 804357000, 9474296896, 99832769119, 999100269973, 9970304382667, 99910262316808, 999100269973000, 9981565340125231, 99912200160380167, 999100269973000000

Offset: 1

Daniel Mondot, Oct 08 2010

Cf. A053058, A180737.

Join[{8,0},Table[Module[{c=Floor[Surd[10^n-1,3]]^3},While[!IntegerQ[ Surd[Total[IntegerDigits[c]],3]],c=(Surd[c,3]-1)^3];c],{n,3,20}]] (* Harvey P. Dale, May 28 2015 *)

Corrected by Arkadiusz Wesolowski at the suggestion of T. D. Noe, Jun 08 2011

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

Original entry on oeis.org

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

K. D. Bajpai, Jan 19 2014

			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.

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

Intersection of A005349 and A053058.

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

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);

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

cp's OEIS Frontend

A237525 Numbers k such that the sum of digits of k^3 is a cube.

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A371004 Fourth powers whose digital sum is also a fourth power.

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A180738 Largest n-digit cube whose sum of digits is also a cube, or 0 if there is no such number.

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

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