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

Author

Gleb Ivanov, Aug 29 2021

Keywords

• nonn
• hard
• more

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.

Examples

			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.
		

Links

• Gleb Ivanov, Rust program for large terms.
• Gleb Ivanov, Python program.

Crossrefs

Cf. A025333, A025419, A025469, A025398.

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

Programs

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 *)

Extensions

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

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