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A349764 a(n) is the smallest number which can be represented as the sum of n distinct n-th powers of primes in exactly n ways.

%I A349764 #22 Dec 22 2021 14:21:32
%S A349764 2,410,8627527,199898912404
%N A349764 a(n) is the smallest number which can be represented as the sum of n distinct n-th powers of primes in exactly n ways.
%e A349764 For n = 2: 410 = 7^2 + 19^2 = 11^2 + 17^2.
%e A349764 For n = 3: 8627527 = 19^3 + 151^3 + 173^3 = 23^3 + 139^3 + 181^3 = 71^3 + 73^3 + 199^3.
%e A349764 From _Michael S. Branicky_, Dec 21 2021: (Start)
%e A349764 For n = 4: 199898912404 =  23^4 + 281^4 + 397^4 + 641^4,
%e A349764                         = 137^4 + 383^4 + 467^4 + 601^4,
%e A349764                         = 151^4 + 227^4 + 557^4 + 563^4,
%e A349764                         = 257^4 + 317^4 + 347^4 + 643^4. (End)
%Y A349764 Cf. A146756.
%K A349764 nonn,hard,bref,more
%O A349764 1,1
%A A349764 _Ilya Gutkovskiy_, Dec 20 2021
%E A349764 a(4) from _Michael S. Branicky_, Dec 21 2021