A226984 Smallest triangular number with exactly n representations as sum of 3 positive cubes.

3, 3655, 260281, 525825, 10656036, 5973696, 980691328, 4971191616, 1004794171200, 110457755136

Offset: 1

Author

Zak Seidov, Jun 25 2013

Keywords

• nonn
• more

Comments

Sequence is apparently infinite.

These triangular numbers are m(m+1)/2 for m = 2, 85, 721, 1025, 4616, 3456, 44287, 99711.

Examples

			n, m, t = m(m+1)/2. t = x^3 + y^3 + z^3:
n = 1, m = 2, t = 3, {x,y,z} = {1,1,1};
n = 2, m = 85, t = 3655, {x,y,z} = {4,6,15}, {9,9,13};
n = 3, m = 721, t = 260281, {x,y,z} = {1,28,62}, {10,42,57}, {15,19,63};
n = 4, m = 1025, t = 525825, {x,y,z} = {1,24,80}, {1,62,66}, {127,59,67}, {48,52,65};
n = 5, m = 4616, t = 10656036, {x,y,z} = {18,115,209}, {27,129,204}, {48,171,177}, {93,159,180}, {111,118,197};
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};
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}.
		

Crossrefs

Cf. A000217 (triangular numbers), A003072 (sums of 3 positive cubes).

Cf. A119977 (triangular numbers that are the sum 3 positive cubes).

Extensions

a(9)-a(10) from Donovan Johnson, Jul 02 2013