A393788 Smallest positive integer expressible as the sum of n distinct positive cubes in n ways with no cube repeated across the representations.

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

Offset

1,2

References

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

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

Links

Table of n, a(n) for n=1..9.

Brennan Benfield, Oliver Lippard, and Arindam Roy, End behavior of Ramanujan's taxicab numbers, arXiv:2404.08190 [math.NT], 2024.

Jeffrey. H. Dinitz, Richard Games, and Robert Roth, Seeds for generalized taxicab numbers, arXiv:1901.09053 [math.NT], 2019.

Abhishek Kumar, Python program

Arup Kumar, Extending OEIS A393788: New Computational Values for a(7), a(8), and a(9), Jul 09 2026.

Example

For n=2: 1729  =  1^3 + 12^3 =  9^3 + 10^3.
For n=3: 12384 =  1^3 + 6^3 + 23^3 =  2^3 + 12^3 + 22^3 =  15^3 + 16^3 + 17^3.
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.
From Michael S. Branicky, Jul 01 2026: (Start)
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.
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)

Prog

(Python) # See link.

Crossrefs

Cf. A000578, A025402, A347362, A350270.

Sequence in context: A154728 A286217 A382809 * A337316 A338998 A280428

Adjacent sequences: A393785 A393786 A393787 * A393789 A393790 A393791

Keyword

nonn,more,changed

Author

Abhishek Kumar, Jun 07 2026

Extensions

a(6) from Michael S. Branicky, Jul 01 2026

a(7)-a(9) from Arup Kumar, Jul 09 2026

Status

approved