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a(n) is the smallest number which can be represented as the sum of n distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.
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%I #15 Jul 09 2024 19:10:34

%S -1,325,5104,16578,70211956,201968338,1690592199245

%N a(n) is the smallest number which can be represented as the sum of n distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.

%e a(2) = 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2.

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

%o (Python)

%o from itertools import count

%o from sympy.solvers.diophantine.diophantine import power_representation

%o def A374257(n): return next(m for m in count(1) if len(list(power_representation(m,n,n)))==3) if n>1 else -1 # _Chai Wah Wu_, Jul 01 2024

%Y Cf. A025304, A025401, A146756, A374227, A374256.

%K sign,more

%O 1,2

%A _Ilya Gutkovskiy_, Jul 01 2024

%E a(7) from _Michael S. Branicky_, Jul 09 2024