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Numbers that are not the sum of 3 nonzero squares and a positive 5th power.
0

%I #4 Jul 08 2020 20:45:47

%S 0,1,2,3,5,6,8,9,11,14,16,17,21,24,26,29,32,33,40,48,64,72,96,112,144,

%T 160,192,240

%N Numbers that are not the sum of 3 nonzero squares and a positive 5th power.

%C No more terms up to 10^6.

%t n = 10^5;

%t t = Union@Flatten@Table[x^2 + y^2 + z^2 + w^5, {x, (n/3)^(1/2)}, {y, x, ((n-x^2)/2)^(1/2)}, {z, y, (n-x^2-y^2)^(1/2)}, {w, 1, (n-x^2-y^2-z^2)^(1/5)}];

%t Complement[Range[0, n], t]

%Y Cf. A000534, A004214, A273915.

%K nonn,more

%O 1,3

%A _XU Pingya_, Jun 17 2020