A347362 Smallest number which can be decomposed into exactly n sums of three distinct positive cubes, but cannot be decomposed into more than one such sum containing the same cube.

36, 1009, 12384, 82278, 746992, 5401404, 15685704, 26936064, 137763072, 251066304, 857520000, 618817536, 3032856000, 2050677000, 6100691904, 36013192704, 16405416000, 96569712000, 48805535232, 131243328000, 611996202000, 201153672000

Offset

1,1

Comments

No cube should appear in two or more sums. 5104 = 15^3 + 10^3 + 9^3 = 15^3 + 12^3 + 1^3 = 16^3 + 10^3 + 2^3 is not a(3), because 15^3 appears in more than one sum.

Links

Table of n, a(n) for n=1..22.

Gleb Ivanov, Rust program for large terms.

Gleb Ivanov, Python program.

Example

a(1) = 36 = 1^3 + 2^3 + 3^3.
a(2) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
a(3) = 12384 = 1^3 + 6^3 + 23^3 = 2^3 + 12^3 + 22^3 = 15^3 + 16^3 + 17^3.

Mathematica

Monitor[Do[k=1; While[Length@Union@Flatten[p=PowersRepresentations[k, 3, 3]]!=n*3||Length@p!=n||MemberQ[Flatten@p, 0], k++]; Print@k, {n, 10}], k] (* Giorgos Kalogeropoulos, Sep 03 2021 *)

Crossrefs

Cf. A025333, A025419, A025469, A025398.

Cf. A343968, A343967, A345088, A345087, A345119, A345152.

Sequence in context: A240685 A294162 A025419 * A180802 A223358 A184292

Adjacent sequences: A347359 A347360 A347361 * A347363 A347364 A347365

Keyword

nonn,hard,more

Author

Gleb Ivanov, Aug 29 2021

Extensions

a(13)-a(15) from Jon E. Schoenfield, Sep 02 2021

a(16)-a(22) from Gleb Ivanov, Sep 12 2021

Status

approved