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Search: id:A000135
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| A000135 |
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Number of partitions into non-integral powers.
(Formerly M1595 N0622)
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+0
1
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| 1, 2, 6, 13, 24, 42, 73, 125, 204, 324, 511, 801, 1228, 1856, 2780, 4135, 6084, 8873, 12847, 18481, 26416, 37473, 52871, 74216, 103596, 143841, 198839, 273654, 374987, 511735, 695559, 941932, 1271139, 1709474, 2291195, 3061385, 4078152, 5416322
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) counts the solutions to the inequality sum_{i=1,2,..} x_i^(2/3)<=n for any number of distinct integers 1<=x_1<x_2<x_3<x_4<... - R. J. Mathar, 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.
Sean A. Irvine, Tentative values of first 55 terms
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EXAMPLE
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For n=3, the 6 solutions are (i) 1^(2/3)<=3. (ii) 1^(2/3)+2^(2/3)<=3. (iii) 2^(2/3)<=3. (iv) 3^(2/3)<=3. (v) 4^(2/3)<=3. (vi) 5^(2/3)<=3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
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CROSSREFS
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Cf. A000148, A000158, A000160.
Sequence in context: A143689 A011891 A003600 this_sequence A065220 A048094 A031872
Adjacent sequences: A000132 A000133 A000134 this_sequence A000136 A000137 A000138
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KEYWORD
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nonn
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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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8 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009
20 more terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Sep 28 2009
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