A000135 Number of partitions into non-integral powers. (Formerly M1595 N0622)

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

Offset

1,2

Comments

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

References

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).

Links

Table of n, a(n) for n=1..38.

B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.

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. [Annotated scanned copy]

Sean A. Irvine, Tentative values of first 55 terms

Example

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. - R. J. Mathar, Jul 03 2009

Crossrefs

Cf. A000148, A000158, A000160.

Sequence in context: A003600 A283551 A362438 * A281865 A267698 A065220

Adjacent sequences: A000132 A000133 A000134 * A000136 A000137 A000138

Keyword

nonn

Author

N. J. A. Sloane

Extensions

8 more terms from R. J. Mathar, Jul 03 2009

20 more terms from Sean A. Irvine, Sep 28 2009

Status

approved