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鞍Ч计

猧孽计厩產谅焊珇吹膀 (Waclaw Sierpinski 1882 - 1969)

(酚The MacTutor History of Mathematics Achievehttp://www-gap.dcs.st-and.ac.uk/~history/ )

鞍Ч计

璝ирЧ计 (Perfect Number) ﹚竡糴р赣计斗ㄤ┮Τ痷羆㎝ (Sum of Aliquot Divisors) э场痷羆㎝и獽Τ┮孔鞍Ч计 (Pseudoperfect Number)鞍Ч计Τ嘿Ч计 (Semiperfect Number)

鞍Ч计猧孽计厩產谅焊珇吹膀 (Waclaw Sierpinski 1882-1969) 矗 20 = 1 + 4 + 5 + 10獽琌ㄒ讽礛鞍Ч计ゑЧ计Ч计ョ琌鞍Ч计栋 (Subset) ㄤ龟ヴЧ计计常穦琌鞍Ч计ぐ或

砞 N Ч计 N = ㄤ┮Τ痷羆㎝ n1 + n2 + n3 + ...

τ k ヴ種俱计kN = kn1 + kn2 + kn3 + ...  kn1 kn2  kn3 单常琌 kN 痷 kN 鞍Ч计

琌ぃ琌┮Τ鞍Ч计АЧ计计㎡ぃ琌и秨﹍穿まㄒ 20 獽ぃ琌ㄤ龟靡癶˙ㄓр靡い N 传鞍Ч计靡Θミ┮┮Τ鞍Ч计计常琌鞍Ч计珿鞍Ч计琌Τ礚ぇ

璝鞍Ч计ぃ琌ㄤ鞍Ч计计и嘿ぇセ鞍Ч计 (Primitive Pseudoperfect Number) ┪セЧ计 (Primitive Semiperfect Number) 6, 20, 28, 88, 104, 272, 304, 350, 368, 464, 490, 496 单 (OEIS A006036 )讽礛Ч计ョ琌セ鞍Ч计い

иョ獶Ч计鞍Ч计ゲ礛琌伦计 (Abundant Number)痷羆㎝ゑō计冈把 伦计莲计㎝Ч计ゅ 

 50 ず鞍Ч计 (ぃ珹Ч计) ㎝ㄤ场だ╊Α(OEIS A005835)

12=
2+4+6 ┪ 1+2+3+6
18=
3+6+9 ┪ 1+2+6+9
20=
1+4+5+10
24=
4+8+12 ┪ 1+3+8+12 ┪ 1+2+3+6+12
30=
5+10+15 ┪ 2+3+10+15 ┪ 1+3+5+6+15
36=
6+12+18 ┪ 2+4+12+18 ┪ 1+2+3+12+18 ┪ 3+6+9+18 ┪ 1+2+6+9+18 ┪ 2+3+4+6+9+12
40=
2+8+10+20 ┪ 1+4+5+10+20 ┪ 1+2+4+5+8+20
42=
7+14+21 ┪ 1+6+14+21
48=
4+8+12+24 ┪ 1+3+8+12+24 ┪ 1+2+3+6+12+24 ┪ 1+3+6+8+12+16 ┪ 1+2+3+4+8+12+16

и鞍Ч计いΤ案计ㄤ龟计ョΤ程ㄒ

 945 = 33 * 5 * 7 = 1 + 5 + 7 + 9 + 15 + 21 + 35 + 45 + 63 + 105 + 135 + 189 + 315Τㄒ (琌セ鞍Ч计のㄤいだ琹Α) 

1575
= 32 * 52 * 7 = 1 + 7 + 9 + 45 + 63 + 75 + 105 + 175 + 225 + 315 + 525
2205
= 32 * 5 * 72 = 3 + 7 + 15 + 35 + 45 + 49 + 63 + 105 + 147 + 245 + 315 + 441 + 735
3465
= 32 * 5 * 7 * 11 = 11 + 15 + 165 + 231 + 315 + 385 + 495 + 693 + 1155
4095
= 32 * 5 * 7 * 13

= 1 + 7 + 15 + 65 + 195 + 273 + 315 + 455 + 585 + 819 + 1365

5355
= 32 * 5 * 7 * 17 = 1 + 21 + 85 + 105 + 255 + 315 + 357 + 595 + 765 + 1071 + 1785
5775
= 3 * 52 * 7 * 11 = 1 + 3 + 5 + 105 + 165 + 175 + 231 + 275 + 385 + 525 + 825 + 1155 + 1925
5985
= 32 * 5 * 7 * 19 = 5 + 21 + 35 + 45 + 63 + 105 + 285 + 315 + 399 + 665 + 855 + 1197 + 1995
6435
= 32 * 5 * 11 * 13 = 1 + 3 + 11 + 45 + 99 + 117 + 143 + 165 + 195 + 429 + 495 + 585 + 715 + 1287 + 2145
6825
= 3 * 52 * 7 * 13

= 1 + 3 + 13 + 65 + 75 + 105 + 175 + 195 + 273 + 325 + 455 + 525 + 975 + 1365 + 2275

7245
= 32 * 5 * 7 * 23 = 23 + 63 + 105 + 207 + 315 + 345 + 483 + 805 + 1035 + 1449 + 2415

把σゅ膍の呼

Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." ”B2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994.

Weisstein, E. W. "Primitive Semiperfect Number." From MathWorld. http://mathworld.wolfram.com/PrimitiveSemiperfectNumber.html.

Weisstein, E. W. "Semiperfect Number." From MathWorld. http://mathworld.wolfram.com/SemiperfectNumber.html.