Practical Number

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, ... (OEIS 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." https://www.dm.unipi.it/gauss-pages/melfi/public_html/pratica.html.

Sloane, N. J. A. Sequence A005153/M0991 in "The On-Line Encyclopedia of Integer Sequences."