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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 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

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