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Triangular numbers that can be written as sum of three positive cubes.
5

%I #14 Sep 23 2024 22:54:50

%S 3,10,36,55,66,136,153,190,253,378,496,528,820,946,1035,1128,1485,

%T 3240,3403,3655,4950,5886,6903,7750,8128,8256,9316,10440,12403,13203,

%U 13861,14365,14535,15051,15753,16290,17020,17205,17578,18915

%N Triangular numbers that can be written as sum of three positive cubes.

%C Intersection of A003072 and A000217.

%H Donovan Johnson, <a href="/A119977/b119977.txt">Table of n, a(n) for n = 1..6577</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%e 153 = 17*(17+1)/2 = 5^3 + 3^3 + 1^3, therefore 153 is a term.

%t Lim=20000;Tlim=Sqrt[2Lim];Clim=Lim^(1/3);Select[Table[n(n+1)/2,{n,Tlim}],MemberQ[Total/@Tuples[Range[Clim]^3,3],#]&] (* _James C. McMahon_, Sep 23 2024 *)

%Y Cf. A113958, A003108, A000578.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 03 2006

%E Two duplicated terms removed by _Donovan Johnson_, Apr 19 2011