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A346115
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Least number k such that k^2 can be expressed in exactly n ways as x^2 + y^4 with {x, y} >= 1.
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9
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OFFSET
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1,1
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COMMENTS
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a(6) <= 15697403475.
2 * 10^10 < a(7) <= 2474052064291275.
These two conjectured values arise from the "green group". Up to term a(5) the least solutions are in the "blue group". Follow the links below to get more information about the different colored groups.
Terms cannot be a square (see the comment from Altug Alkan in A111925).
Terms must have at least one prime factor of the form p == 1 (mod 4), a Pythagorean prime (A002144).
If the terms additionally have prime factors of the form p == 3 (mod 4), which are in A002145, then they must appear in the prime divisor sets of x and y too. The special prime factor 2 has the same behavior, i.e., if the term is even, x and y must be even too. (End)
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LINKS
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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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