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A319052
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Numbers that are not the sum of {2 squares, a nonnegative cube, and a nonnegative k-th power with k >= 17}.
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1
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OFFSET
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1,1
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COMMENTS
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Except for the above 7 terms, the remaining 427 numbers in A022552 can be expressed as the sum of two squares, a nonnegative cube and a nonnegative k-th power. So a(n) has only 7 terms, until n = 10^10.
Also, for n <= 6*10^7, when k = 3, the number of such forms is only 23; when 4 <= k <= 5, only 23 and 71; when k = 6, only 23, 71 and 455; when 7 <= k <= 8, only 23, 71 and 120; when 9 <= k <= 11, only 23, 71, 120, 312 and 455; when 12 <= k <= 16, only 23, 71, 120, 312, 455 and 2136.
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LINKS
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MATHEMATICA
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n=100000;
t=Union@Flatten@Table[x^2+y^2+z^3+w^17, {x, 0, n^(1/2)}, {y, x, (n-x^2)^(1/2)}, {z, 0, (n-x^2-y^2)^(1/3)}, {w, 0, (n-x^2-y^2-z^3)^(1/17)}];
Complement[Range[0, n], t]
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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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