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A000148
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Number of partitions into non-integral powers.
(Formerly M1743 N0691)
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5
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1, 2, 7, 15, 28, 45, 70, 100, 138, 183, 242, 310, 388, 481, 583, 701, 838, 984, 1152, 1337, 1535, 1757, 2001, 2262, 2545, 2855, 3183, 3540, 3926, 4335, 4770, 5233, 5728, 6248, 6801, 7388, 8005, 8658, 9345, 10064, 10824, 11620, 12452, 13324, 14236
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OFFSET
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2,2
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COMMENTS
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a(n) is the number of solutions to the inequality x_1^(2/3) + x_2^(2/3) <= n where 1 <= x_1 <= x_2 are any two integers. If the number of terms in the sum is not restricted to 2, we get A000234. - R. J. Mathar, Jul 03 2009
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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A000148[n_] := Sum[Min[xi, Floor[(n - xi^(2/3))^(3/2)]], {xi, 1, Floor[n^(3/2)]}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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