5/29/2017 Tables of Aliquot Cycles http://amicable.homepage.dk/tables.htm Go FEB MAY JUN f ❎ 117 captures 02 ⍰ ▾ About 28 May 2002 ‑ 2 May 2014 2012 2014 2015 this capture Tables of Aliquot Cycles

Click on the number of known cycles to view the corresponding lists.

Sociable Sociable Numbers Amicable Numbers Numbers Perfect Numbers of order four Type of other orders Known Last Known Last Known Last Known Last Cycles Update Cycles Update Cycles Update Cycles Update 28­Sep­ 01­Oct­ 13­Nov­ 11­Sep­ Ordinary 11994387 142 10 44 2007 2007 2006 2006 28­Sep­ 20­Nov­ 14­Jun­ 14­Dec­ Unitary 4911908 191 24 5 2007 2006 2005 1997 28­Sep­ 28­Sep­ 20­Nov­ 28­Sep­ Infinitary 11538100 5034 129 190 2007 2007 2006 2007 Exponential (note 3089296 28­Sep­ 371 20­Nov­ 38 15­Jun­ 12 06­Dec­ 2) 2007 2006 2005 1998 05­Feb­ 08­May­ 18­Oct­ 11­Mar­ Augmented 1931 2 0 note 1 2002 2003 1997 1998 05­Feb­ 06­Dec­ 06­Dec­ Augmented Unitary 27 0 0 2002 1998 1998 Augmented 10­Sep­ 06­Dec­ 06­Dec­ 425 0 0 Infinitary 2003 1998 1998 15­Feb­ 18­Oct­ 18­Oct­ 11­Mar­ Reduced 1946 0 1 0 2003 1997 1997 1998 Reduced Unitary 28 15­Feb­ 0 06­Dec­ 0 06­Dec­

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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.

Exhaustive limits

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.

Amicable Numbers Sociable Numbers Perfect Numbers Type Exhaustive below Exhaustive below Exhaustive below Ordinary 1014 51012 10300 Unitary 21012 21011 (21012) Infinitary 51012 21011 (51012) Exponential (41011) (41011) (41011) Augmented 1012 21011 (1012) Augmented Unitary 21011 21011 Augmented Infinitary 21011 21011 Reduced 1012 21011 1035 http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm 2/3 5/29/2017 Tables of Aliquot Cycles Reduced Unitary http://amicable.homepage.dk/tables.htm21011 21011 Go FEB MAY JUN f ❎ 117 captures 11 11 02 ⍰ Reduced Infinitary 210 210 ▾ About 28 May 2002 ‑ 2 May 2014 2012 2014 2015 this capture

Links

Perfect, amicable, and sociable numbers (how to have fun summing up divisors) by David Moews Amicable Pair, Sociable Numbers, Perfect Number, Unitary Amicable Pair, Unitary Sociable Numbers, Unitary Perfect Number, Infinitary Perfect Number, e­Perfect Number, Augmented Amicable Pair, Almost Perfect Number, Quasiamicable Pair, Quasiperfect Number by Eric W. Weisstein Aliquot Sequences by Wolfgang Creyaufmüller (same in German)

Last update: 01­Oct­2007

Jan Munch Pedersen, [email protected]

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