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A332664
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a(n) = number of nonnegative integers that are not the sum of {2 squares, a nonnegative 5th power, and a nonnegative n-th power}.
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0
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0, 2, 14, 115, 116, 109, 245, 381, 1387, 913, 1234, 1552, 2103, 2838, 3036, 3384, 4693, 5405, 8304, 9088, 11089, 13289, 15815, 18619, 20979, 22755, 24107, 24984, 25548
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OFFSET
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2,2
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COMMENTS
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a(2) = 0 by a theorem of Zhi-Wei Sun, see A273915. All terms beyond a(2) are conjectures and have only been checked to 4*10^9.
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LINKS
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EXAMPLE
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a(2) = 0, since any nonnegative integer k is the sum of 3 squares and a nonnegative 5th power (see A273915).
a(4) = 14. Since any nonnegative integer k (<= 4*10^9) is the sum of {2 squares, a nonnegative 5th power, and a 4th power}, except for 14 numbers: 23, 44, 71, 79, 215, 383, 863, 1439, 1583, 1727, 1759, 1919, 2159, 2543.
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MATHEMATICA
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a(5)
Do[m=1000000 (k-1)+1; n=1000000 k;
t=Union@Flatten@Table[x^2 + y^2 + z^5 + w^5,
{x, 0, n^(1/2)}, {y, x, (n-x^2)^(1/2)}, {z, 0, (n-x^2-y^2)^(1/5)},
{w, If[x^2 + y^2 + z^5 < m, Floor[(m-1-x^2-y^2-z^5)^(1/5)] + 1, z], (n-x^2-y^2-z^5)^(1/5)}];
b=Complement[Range[m, n], t];
Print[Length@b], {k, 4000}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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