A number is practical if for all , is the sum of distinct proper divisors of . Defined in 1948 by
A. K. Srinivasen. All even Perfect Numbers are practical. The number

is practical for all , 3, .... The first few practical numbers are 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, ... (Sloane's A005153). G. Melfi has computed twins, triplets, and 5-tuples of practical numbers. The first few 5-tuples are 12, 18, 30, 198, 306, 462, 1482, 2550, 4422, ....

**References**

Melfi, G. ``On Two Conjectures About Practical Numbers.'' *J. Number Th.* **56**, 205-210, 1996.

Melfi, G. ``Practical Numbers.'' http://www.dm.unipi.it/gauss-pages/melfi/public_html/pratica.html.

Sloane, N. J. A. Sequence
A005153/M0991
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