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A274132 Numbers m such that m^k is the sum of three positive cubes for all positive integers k. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Jun 10 2016
STATUS
approved

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Last modified June 1 18:23 EDT 2023. Contains 363076 sequences. (Running on oeis4.)