A066215 Numbers which are sums of cubes of some subset of divisors.

1, 8, 27, 36, 64, 72, 125, 216, 252, 288, 343, 378, 512, 520, 576, 584, 729, 738, 756, 792, 828, 855, 954, 972, 1000, 1044, 1331, 1350, 1440, 1520, 1540, 1728, 1764, 1800, 1890, 1944, 1980, 2016, 2070, 2160, 2197, 2304, 2352, 2376, 2400, 2484, 2520, 2548

Offset

1,2

Comments

There are cubes that have not a single, trivial representation but more than one. These start with 27000 =+8^3+9^3+10^3+12^3+15^3+18^3+24^3 =+1^3+2^3+4^3+6^3+8^3+10^3+15^3+20^3+24^3 = +2^3+4^3+9^3+10^3+15^3+20^3+24^3 =+1^3+2^3+4^3+12^3+15^3+20^3+24^3 =+2^3+3^3+4^3+5^3+6^3+12^3+15^3+18^3+25^3 =+1^3+4^3+5^3+6^3+8^3+9^3+12^3+20^3+25^3 =+15^3+20^3+25^3 = +1^3+3^3+6^3+8^3+9^3+18^3+27^3 =+30^3 and 46656 =+1^3+2^3+3^3+6^3+8^3+9^3+12^3+16^3+18^3+24^3+27^3 =+4^3+24^3+32^3 =+36^3 and 74088 =+2^3+6^3+7^3+8^3+9^3+12^3+18^3+21^3+24^3+27^3+28^3 =+4^3+6^3+8^3+14^3+18^3+21^3+24^3+27^3+28^3 =+42^3. - R. J. Mathar, Jan 21 2024

If m is in the sequence then so is m*k^3 for k >= 1. - David A. Corneth, Jan 21 2024

Links

David A. Corneth, Table of n, a(n) for n = 1..10286 (first 649 terms from R. J. Mathar)

R. J. Mathar, Examples/decompositions for entries <10000

Example

72 is in the list since 72 = 2^3 + 4^3 and 2 and 4 are divisors of 72

Mathematica

okQ[k_] := AnyTrue[Subsets[Select[Divisors[k]^3, # <= k&]], Total[#]==k&];
Reap[For[k = 1, k <= 10000, k++, If[okQ[k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, May 27 2024 *)

Crossrefs

Cf. A000578, A066214, A066213, A066216.

Sequence in context: A213519 A352423 A371955 * A086213 A175050 A063142

Adjacent sequences: A066212 A066213 A066214 * A066216 A066217 A066218

Keyword

nonn

Author

Erich Friedman, Dec 17 2001

Status

approved