A393788 - OEIS

A393788

Smallest positive integer expressible as the sum of n distinct positive cubes in n ways with no cube repeated across the representations.

%I #79 Jul 12 2026 00:23:13

%S 1,1729,12384,13104,37656,84825,271998,646759,1225449

%N Smallest positive integer expressible as the sum of n distinct positive cubes in n ways with no cube repeated across the representations.

%D B. Benfield, O. Lippard and A. Roy, End behavior of Ramanujan's taxicab numbers, The Ramanujan Journal, 66 (1) (2025), 17.

%D S. S. Wagstaff Jr., Ramanujan's taxicab number and its ilk, The Ramanujan Journal, 64 (3) (2024), 761-764.

%H Brennan Benfield, Oliver Lippard, and Arindam Roy, <a href="https://arxiv.org/abs/2404.08190">End behavior of Ramanujan's taxicab numbers</a>, arXiv:2404.08190 [math.NT], 2024.

%H Jeffrey. H. Dinitz, Richard Games, and Robert Roth, <a href="https://arxiv.org/abs/1901.09053">Seeds for generalized taxicab numbers</a>, arXiv:1901.09053 [math.NT], 2019.

%H Abhishek Kumar, <a href="/A393788/a393788_1.py.txt">Python program</a>

%H Arup Kumar, <a href="https://doi.org/10.5281/zenodo.21273630">Extending OEIS A393788: New Computational Values for a(7), a(8), and a(9)</a>, Jul 09 2026.

%e For n=2: 1729 = 1^3 + 12^3 = 9^3 + 10^3.

%e For n=3: 12384 = 1^3 + 6^3 + 23^3 = 2^3 + 12^3 + 22^3 = 15^3 + 16^3 + 17^3.

%e For n=4: 13104 = 1^3 + 11^3 + 17^3 + 19^3 = 2^3 + 10^3 + 16^3 + 20^3 = 5^3 + 7^3 + 15^3 + 21^3 = 6^3 + 8^3 + 12^3 + 22^3.

%e From _Michael S. Branicky_, Jul 01 2026: (Start)

%e For n=5: 37656 = 2^3 + 15^3 + 20^3 + 22^3 + 25^3 = 4^3 + 9^3 + 14^3 + 23^3 + 28^3 = 5^3 + 12^3 + 19^3 + 21^3 + 27^3 = 6^3 + 8^3 + 16^3 + 18^3 + 30^3 = 7^3 + 10^3 + 17^3 + 24^3 + 26^3.

%e For n=6: 84825 = 1^3 + 2^3 + 8^3 + 22^3 + 30^3 + 36^3 = 3^3 + 6^3 + 7^3 + 23^3 + 32^3 + 34^3 = 4^3 + 10^3 + 14^3 + 16^3 + 20^3 + 41^3 = 5^3 + 12^3 + 15^3 + 21^3 + 27^3 + 37^3 = 9^3 + 17^3 + 19^3 + 24^3 + 25^3 + 35^3 = 11^3 + 13^3 + 18^3 + 26^3 + 28^3 + 33^3. (End)

%o (Python) # See link.

%Y Cf. A000578, A025402, A347362, A350270.

%K nonn,more,changed

%O 1,2

%A _Abhishek Kumar_, Jun 07 2026

%E a(6) from _Michael S. Branicky_, Jul 01 2026

%E a(7)-a(9) from _Arup Kumar_, Jul 09 2026