Click on the number of known cycles to view the corresponding lists.
| Type | Amicable Numbers | Sociable Numbers of order four |
Sociable Numbers of other orders |
Perfect Numbers | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Known Cycles |
Last Update |
Known Cycles |
Last Update |
Known Cycles |
Last Update |
Known Cycles |
Last Update |
|||||
| Ordinary | 11994387 | 28-Sep-2007 | 142 | 01-Oct-2007 | 10 | 13-Nov-2006 | 44 | 11-Sep-2006 | ||||
| Unitary | 4911908 | 28-Sep-2007 | 191 | 20-Nov-2006 | 24 | 14-Jun-2005 | 5 | 14-Dec-1997 | ||||
| Infinitary | 11538100 | 28-Sep-2007 | 5034 | 28-Sep-2007 | 129 | 20-Nov-2006 | 190 | 28-Sep-2007 | ||||
| Exponential (note 2) | 3089296 | 28-Sep-2007 | 371 | 20-Nov-2006 | 38 | 15-Jun-2005 | 12 | 06-Dec-1998 | ||||
| Augmented | 1931 | 05-Feb-2002 | 2 | 08-May-2003 | 0 | 18-Oct-1997 | note 1 | 11-Mar-1998 | ||||
| Augmented Unitary | 27 | 05-Feb-2002 | 0 | 06-Dec-1998 | 0 | 06-Dec-1998 | ||||||
| Augmented Infinitary | 425 | 10-Sep-2003 | 0 | 06-Dec-1998 | 0 | 06-Dec-1998 | ||||||
| Reduced | 1946 | 15-Feb-2003 | 0 | 18-Oct-1997 | 1 | 18-Oct-1997 | 0 | 11-Mar-1998 | ||||
| Reduced Unitary | 28 | 15-Feb-2003 | 0 | 06-Dec-1998 | 0 | 06-Dec-1998 | ||||||
| Reduced Infinitary | 427 | 10-Sep-2003 | 0 | 06-Dec-1998 | 0 | 06-Dec-1998 | ||||||
Note 1: All powers of 2 are augmented perfect numbers; no other augmented perfect numbers are known.
Note 2: Multiplying all members of an exponential aliquot cycle by a squarefree number prime to all the members of the cycle yields a new exponential aliquot cycle. Cycles that can be constructed from other cycles this way aren't listed (nor counted).
Some of the discoverer information in the lists might still be wrong. All kind of updates are welcome. A great thanks to David Moews for sending me a lot of discoverer information.
This table indicates how far exhaustive searchs for the various kinds of cycles has been carried. For amicable numbers all pairs with smaller member below the limit are known. For sociable numbers all cycles with the member preceeding the largest member below the limit are known.
| Type | Amicable Numbers Exhaustive below |
Sociable Numbers Exhaustive below |
Perfect Numbers Exhaustive below |
|||
|---|---|---|---|---|---|---|
| Ordinary | 1014 | 5×1012 | 10300 | |||
| Unitary | 2×1012 | 2×1011 | (2×1012) | |||
| Infinitary | 5×1012 | 2×1011 | (5×1012) | |||
| Exponential | (4×1011) | (4×1011) | (4×1011) | |||
| Augmented | 1012 | 2×1011 | (1012) | |||
| Augmented Unitary | 2×1011 | 2×1011 | ||||
| Augmented Infinitary | 2×1011 | 2×1011 | ||||
| Reduced | 1012 | 2×1011 | 1035 | |||
| Reduced Unitary | 2×1011 | 2×1011 | ||||
| Reduced Infinitary | 2×1011 | 2×1011 | ||||
Last update: 01-Oct-2007
Jan Munch Pedersen, amicable@post.cybercity.dk