[]nФơnȤ٤Ƥ¤nȰפȤnȤ
[]n٤Ƥ¤(n)Ƚ
[]nǤȤ(n)=2nΩġ
[]n=6ϴǤ롣ʤʤС61,2,3,6Ǥꡢ6Ȥȡ1+2+3=6Ȥʤ뤫Ǥ롣
[]nǰʬn=paqbrcĤȤС(n)ϼμǷǤ롣
[]˼Ѥͤ롣
(1+p++pa)(1+q++qb)(1+r++rc)
Ÿݤ˸ƹpqrĤˤꡢnʽʣʤˤ٤Ϳ롣
ʤʤС[]ֹnǰʬn=paqbrcĤȤСΤpqrġ0a0¡b0ácĤͿפΩĤ顣
äơѤͤϦ(n)
(n)=(1+p++pa)(1+q++qb)(1+r++rc)
ˡθ
ŬѤСΩġ
[]n=496ɤĴ٤롣
nǤС֦(n)=2nפΩĤᡢޤ(n)롣
496=2431ǰʬǤΤǡ(496)ϼΤ褦ˤƷǤ롣
(496)
=
=(32-1)(31+1)
=3125
=2496
äơ496ϴǤ롣
[]
pǿMp륻ǿMp=2p-1ˤȤ롣
ΤȤMp2p-1͡ʴˤʤˤ1ΰ̤6 or 8Ǥ롣
[]2Τ٤ϼΤ褦ˤʤ롣
2,22=4,23=8,24=16,25=32
äơ2p-11ΰ̤2,4,6,8Τɤ줫Ǥ롣
2p-11ΰ | 2 | 4 | 6 | 8 | |
2p1ΰ | 4 | 8 | 2 | 6 | 嵭ιԤ2ܤ̤1ΰ |
2p-11ΰ | 3 | 7 | 1 | 5 | 륻ǿθ䡣嵭ιԤ-1̤1ΰ |
(2p-1)2p-11ΰ | 6 | 8 | 6 | 0 | ־ιԤ1ľιԤ軻̤1ΰ |
2p-11ΰ̤ο5ξˤϡ2p-1ǿǤϤʤ
ʤʤС1ΰ̤ο5ǿǤϡ5ΤȤꤨʤ2p-1=5p¸ߤʤǤ롣
äơ2p-1ϥ륻ǿǤϤʤΤǡ롣
äơMp2p-1ͤ1ΰ̤6 or 8Ǥ롣
[]̤
δ¸ߤʤ
[]¸ߤС10300ʾοǤ롣
[]̤
̵¸¸ߤ롣
[]륻ǿ̵¤ˤ뤫狼äƤʤ⤷̵¤ˤСδ̵¤ˤ뤳Ȥˤʤ롣