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a(n) is the smallest number which can be represented as the sum of 4 distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.
11

%I #8 Jul 16 2024 16:14:45

%S 13,78,1521,16578,1479604544,1885800643779

%N a(n) is the smallest number which can be represented as the sum of 4 distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.

%e a(4) = 16578 = 1^4 + 2^4 + 9^4 + 10^4 = 2^4 + 5^4 + 6^4 + 11^4 = 3^4 + 7^4 + 8^4 + 10^4.

%e a(5) = 1479604544 = 3^5 + 48^5 + 52^5 + 61^5 = 13^5 + 36^5 + 51^5 + 64^5 = 18^5 + 36^5 + 44^5 + 66^5.

%Y Cf. A046881, A374418, A374421, A374422, A374423, A374424.

%K nonn,hard,more

%O 1,1

%A _Ilya Gutkovskiy_, Jul 08 2024

%E a(6) from _Michael S. Branicky_, Jul 09 2024