gives the number of ways of writing the Integer as a sum of Positive Integers without regard to order with the constraint that all Integers in each sum are distinct. The values for , 2, ... are 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, ... (Sloane's A000009). The Generating Function for is

The values of for which is Prime are 3, 4, 5, 7, 22, 70, 100, 495, 1247, 2072, ... (Sloane's A046065), with no others for .

The number of Partitions of with summands is denoted or
. Therefore, and

**References**

Abramowitz, M. and Stegun, C. A. (Eds.). ``Partitions into Distinct Parts.'' §24.2.2 in
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 823-824, 1972.

Sloane, N. J. A. Sequences
A046065 and
A000009/M0281
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26