[seqfan] Partitions into non-integral powers

franktaw at netscape.net franktaw at netscape.net
Fri Jul 3 05:20:43 CEST 2009

There are 12 sequences (A000135, A000148, A000158, A000160, A000263, 
A000298, A000327, A000333, A000339, A000345, A000347, and A000397) with 
the title "Number of partitions into non-integral powers".  A000234, 
with title "Partitions into non-integral powers (see Comments for 
precise definition)." has an explanation (thanks to Richard Mather); 
none of these others do.

All these sequences reference a paper: "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.".  Sequence 
A000093, "[ n^(3/2) ]" (which should really be "floor(n^(3/2))" also 
references this paper, although there is no obvious connection.

It would be nice if somebody could look at this paper and provide 
explanations for the remaining sequences.

Franklin T. Adams-Watters

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