Ч计

縩Ч计

Ч计 (Perfect Number)  s(N)=2N 璝ир硂阀├崩約縩Ч计 (Multiperfect Number) s(N)=kNи獽嘿 k 縩Ч计(k-multiperfect Number)璝 k = 2 獽琌炊硄Ч计セ彻癚阶 k > 2 薄猵

 k=3 672 琌ㄒ弄︽喷靡ゑウ临Τ 120

 k=4 2178540 琌ㄒㄤだ秆Α 22 * 32 * 5 * 72 * 13 * 19

场だㄒㄑ把σ

縩Ч计 N
计 k
120
3
30240
4
14182439040
5
(223)(37)(52)(74)(113)(172)(31)(41)(61)(241)(307)(467)(2801)
6

(246)(315)(53)(75)(11)(13)(17)(194)(23)(31)(37)(41)(43)(61)(89)(97)(151)(193)(911)(2351)(4513)

(442151)(13264529)

7

ㄓ縩Ч计计 k 蝴 8 ゼΤ瘆ㄤい城狥 (Stephen Gretton) т硂妓 8-縩Ч计

(262)(315)(59)(72)(113)(172)(19)(23)(29)(312)(37)(41)(43)(53)(612)(712)(73)(83)(89)(972)(127)(193)(283)(307)(317)

(331)(337)(487)(5212)(601)(1201)(1279)(2557)(3169)(5113)(92737)(649567)

硂ョ獺琌程 8-縩Ч计度 126 计τ

 1992-1993丁ェ吹 (Fred W. Helenius) т碭 9-縩Ч计ㄒ程琌

(2114)(335)(517)(712)(114)(135)(173)(198)(232)(292)(312)(374)(41)(43)(472)(53)(612)(67)(71)(73)(792)(832)(892)(97)

(103)(109)(127)(1312)(151)(157)(167)(1792)(197)(211)(227)(331)(347)(367)(379)(443)(523)(599)(709)(757)(829)

(1151)(1699)(1789)(2003)(2179)(2999)(3221)(4271)(4357)(4603)(5167)(8011)(8647)(8713)(14951)(17293)(21467)

(29989)(110563)(178481)(530713)(672827)(4036961)(218834597)(16148168401)(151871210317)

(2646507710984041)

硂琌 326 计俱计

禬Ч计

孔禬Ч计 (Superperfect Number) 

и笵Ч计 (Perfect Number) ﹚竡琌 s(N)=2N璝ир s(N) эΘ sk(N)  s(s(......s(N).....)) р硂ㄧ计 (Function) 甅 k Ω璝Τ计 N 骸ì sk(N) =2N 杠硂 N 獽琌 k禬Ч计 (k-Superperfect Number) 礛τ硂琌

и讽礛р琾Ч计 (Almost Perfect Number) ㎝ 览Ч计 (Quasi-perfect Number) ﹚竡まビ筁ㄓ璝Τ计 N 骸ì sk(N) =2N-1 ê獽琌琾禬Ч计 (Almost-superperfect Number) ┪Τ计 N 骸ì sk(N) =2N+1 ê獽琌览禬Ч计 (Quasi-superperfect Number)拜硂琌

计厩產さごゼт禬Ч计

じЧ计

じЧ计 (Unitary Perfect Number) 琌ぐ或

じЧ计иσ納痷じ羆㎝ (Sum of Aliquot Unitary Divisors)

じ (Unitary Divisor) 琌ぐ或

琘计 N じ d ㄏ N/d 籔 d が (Coprime) 20  1, 2, 4, 5, 10, 20 い 1, 4, 5, 20 じи┪硂妓弧 N だ秆Α (Prime Factorization) い癸ヴ计 p иσ納 pk τ k 琌赣计 N 程蔼Ωよ硂妓 pk ┪ ウ縩獽琌じ

τ痷じ (Aliquot Unitary Divisors) ぃ珹赣计セōㄤウじ

 60 60 = 22 * 3 * 5 ┮ 60 じΤ 1, 3, 4 = 22, 5, 12 = 22 * 3, 15 = 3 * 5, 20 = 22 * 5, 60 = 22 * 3 * 5τ 60 = 1 + 3 + 4 + 5 + 12 + 15 + 20珿 60 獽琌ㄤいじЧ计

じЧ计临Τ 6, 60, 90, 87360, 146361946186458562560000 单(OEIS A002827)

肈杠じЧ计約狥杠弄ㄓ会露硂㎝妓计摸 钵计 (Odd Weird Number) 弄猭妓露ㄢ瘤礚闽玒иぃ筁祅約τ璝稱秈˙秆ê钵计Τ钵把鞍Ч计