A000148 Number of partitions into non-integral powers. (Formerly M1743 N0691)

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

Offset

2,2

Comments

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

References

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

Seth A. Troisi, Table of n, a(n) for n = 2..1000

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.

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]

Mathematica

A000148[n_] := Sum[Min[xi, Floor[(n - xi^(2/3))^(3/2)]], {xi, 1, Floor[n^(3/2)]}];
Table[A000148[n], {n, 2, 100}] (* Seth A. Troisi, May 25 2022 *)

Crossrefs

Cf. A000158, A000160, A000327.

Sequence in context: A061802 A263603 A003452 * A147672 A246790 A289939

Adjacent sequences: A000145 A000146 A000147 * A000149 A000150 A000151

Keyword

nonn,changed

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Oct 08 2009

Status

approved