1,2

a(n) is the number of solutions to the inequality sum_{i=1,2,..} x_i^(1/2)<=n for unknowns 1<=x_1<x_2<x_3<x_4<.... [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

The 12 solutions for n=3 are 1^(1/2)<=3, 1^(1/2)+2^(1/2)<=3, 1^(1/2)+3^(1/2)<=3, 1^(1/2)+4^(1/2)<=3, 2^(1/2)<=3, 3^(1/2)<=3,...,8^(1/2)<=3 and 9^(1/2)<=3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]

Sequence in context: A037166 A118892 A100691 this_sequence A006802 A068055 A074252

Adjacent sequences: A000295 A000296 A000297 this_sequence A000299 A000300 A000301

nonn

N. J. A. Sloane (njas(AT)research.att.com).

3 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009