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a(n) is the smallest number which can be represented as the sum of n distinct nonzero fourth powers in exactly 2 ways, or -1 if no such number exists.
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%I #9 Jul 16 2024 16:14:50

%S -1,635318657,6578,6834,7459,8755,18755,23412,43893,53893,92309,

%T 123335,182566,232647,298183,393848,521849,681849,872105,1066586,

%U 1343612,1623453,1955229,2412205,2811596,3424941,4132222

%N a(n) is the smallest number which can be represented as the sum of n distinct nonzero fourth powers in exactly 2 ways, or -1 if no such number exists.

%e a(2) = 635318657 = 59^4 + 158^4 = 133^4 + 134^4.

%e a(3) = 6578 = 1^4 + 2^4 + 9^4 = 3^4 + 7^4 + 8^4.

%Y Cf. A000538, A003824, A360306, A374287, A374417.

%K sign,more

%O 1,2

%A _Ilya Gutkovskiy_, Jul 12 2024

%E a(18)-a(27) from _Michael S. Branicky_, Jul 13 2024