A274132 Numbers m such that m^k is the sum of three positive cubes for all positive integers k.

134, 153, 216, 225, 244, 251, 288, 342, 368, 405, 408, 415, 528, 532, 540, 577, 645, 729, 750, 755, 764, 855, 863, 882, 918, 919, 946, 972, 980, 1065, 1072, 1080, 1126, 1224, 1250, 1333, 1351, 1422, 1457, 1464, 1466, 1520, 1539, 1548, 1581, 1611, 1701, 1728

Offset

1,1

Comments

Cubes in this sequence are 216, 729, 1728, 5832, 6859, ...

If m, m^2 and m^3 are sums of three positive cubes, then m is in the sequence, because if m^k = a^3 + b^3 + c^3, m^(3+k) = (m*a)^3 + (m*b)^3 + (m*c)^3. - Robert Israel, Jul 02 2019

Links

Table of n, a(n) for n=1..48.

Example

134 is a term because 134 = 1^3 + 2^3 + 5^3, 134^2 = 10^3 + 11^3 + 25^3, 134^3 = 44^3 + 102^3 + 108^3, 134^4 = 134^3 + (2*134)^3 + (5*134)^3, 134^5 = 1340^3 + (11*134)^3 + (25*134)^3, ...

Maple

A3072:= proc(n) local a, b, c;
  for a from 1 while 3*a^3<=n do
   for b from a while a^3 + 2*b^3 <= n do
     c:= floor((n-a^3-b^3)^(1/3));
     if a^3+b^3+c^3=n then return true fi;
 od od;
 false
end proc:
filter:= n -> A3072(n) and A3072(n^2) and A3072(n^3):
select(filter, [$1..2000]); # Robert Israel, Jul 02 2019

Mathematica

A3072[n_] := Module[{a, b, c}, For[a = 1, 3 a^3 <= n, a++, For[b = a, a^3 + 2 b^3 <= n, b++, c = Floor[(n - a^3 - b^3)^(1/3)]; If[a^3 + b^3 + c^3 == n, Return[ True]]]]; False];
okQ[n_] := If[A3072[n] && A3072[n^2] && A3072[n^3], Print[n]; True, False];
Select[Range[2000], okQ] (* Jean-François Alcover, Feb 10 2023, after Robert Israel *)

Crossrefs

Cf. A003072.

Sequence in context: A191715 A208626 A061491 * A252133 A255795 A048128

Adjacent sequences: A274129 A274130 A274131 * A274133 A274134 A274135

Keyword

nonn

Author

Altug Alkan, Jun 10 2016

Status

approved