A025398 -id:A025398 - cp's OEIS frontend

A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

5104, 5832, 9288, 9729, 10261, 10773, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24416, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 39528, 40060, 40097, 40832, 40851, 41033, 41040, 41364

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 11 2013

nonn

Index of A051343 = 9, superset of index of A025456 = 3.

Subset of A001239.

			a(1) = 5104 = 1^3+12^3+15^3 = 2^3+10^3+16^3 = 9^3+10^3+15^3.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Decomposition of the first 10000 terms into 3 sets of cube triples
Sequences related to sums of squares and cubes

Other sums of cubes: A025402, A025398, A024974, A001239, A008917.
Cf. A025456, A051343.
Cf. A025396.

Select[Range[42000],Length[PowersRepresentations[#,3,3]]==3&] (* Harvey P. Dale, Sep 28 2016 *)

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.

Original entry on oeis.org

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

Offset: 1

Gleb Ivanov, Aug 29 2021

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.

			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.

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

Cf. A025333, A025419, A025469, A025398.

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

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 *)

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

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

cp's OEIS Frontend

A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

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