login
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.
1
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.
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 *)
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