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Search: id:A000148
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| A000148 |
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Number of partitions into non-integral powers.
(Formerly M1743 N0691)
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+0
3
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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
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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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 A000298. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
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REFERENCES
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B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
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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B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
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CROSSREFS
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Adjacent sequences: A000145 A000146 A000147 this_sequence A000149 A000150 A000151
Sequence in context: A113422 A061802 A003452 this_sequence A147672 A095091 A131412
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 08 2009
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