%I
%S 3,3655,260281,525825,10656036,5973696,980691328,4971191616,
%T 1004794171200,110457755136
%N Smallest triangular number with exactly n representations as sum of 3 positive cubes.
%C Sequence is apparently infinite.
%C These triangular numbers are m(m+1)/2 for m = 2, 85, 721, 1025, 4616, 3456, 44287, 99711.
%e n, m, t = m(m+1)/2. t = x^3 + y^3 + z^3:
%e n = 1, m = 2, t = 3, {x,y,z} = {1,1,1};
%e n = 2, m = 85, t = 3655, {x,y,z} = {4,6,15}, {9,9,13};
%e n = 3, m = 721, t = 260281, {x,y,z} = {1,28,62}, {10,42,57}, {15,19,63};
%e n = 4, m = 1025, t = 525825, {x,y,z} = {1,24,80}, {1,62,66}, {127,59,67}, {48,52,65};
%e n = 5, m = 4616, t = 10656036, {x,y,z} = {18,115,209}, {27,129,204}, {48,171,177}, {93,159,180}, {111,118,197};
%e n = 6, m = 3456, t = 5973696, {x,y,z} = {3,114,165}, {8,96,172}, {12,144,144}, {39,65,178}, {72,80,172}, {108,120,144};
%e n = 7, m = 44287, t = 980691328, {x,y,z} = {64,396,972}, {86,250,988}, {163,208,989}, {184,524,940}, {225,478,951}, {550,634,824}, {662,667,733}.
%Y Cf. A000217 (triangular numbers), A003072 (sums of 3 positive cubes).
%Y Cf. A119977 (triangular numbers that are the sum 3 positive cubes).
%K nonn,more
%O 1,1
%A _Zak Seidov_, Jun 25 2013
%E a(9)a(10) from _Donovan Johnson_, Jul 02 2013
