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基于最大素数幂分解的n表示

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A基于最大素数幂分解的n表示具有主要权力向右增加(类似于基b表示法)

{0,1,10,100,1000,11,10000,100000,1000000,1001,10000000,110,100000000,10001,10101000000,1000000000,1000000000,10000000000,1100,10010,10000001,}

它可以用基数8表示,将三个二进制数字组合成一个八进制数字

{0,1,2,4,10,3,20,40,100,11,200,6,400,21,12,1000,2000,101,4000,14,22,201,10000,42,20000,401,40000,24,100000,13,200000,}

下表给出。请注意,尽管表示在所需的数字集(即二进制版本的{0,1})中是非常经济的,但是在所需的位数方面,它是非常不经济的,直到n以下素数幂,它对n以下素数,即。,使得这种表述绝对不切实际!(参见。A025528号)

现在,如果你想创造一个正整数的排序通过增加基于最大素数幂分解的n表示,我们有一个恼人的问题,就是处理表示的不可接受值,例如101将(向右)8表示为2乘以4,这不是8的因式分解中的最大素数幂。我们没有一对一通信正整数(作为最大素数幂的乘积)和非负整数(作为基于最大素数幂分解的n表示)但是有一个解决方法:通过考虑素数幂的指数是基2表示,这相当于只考虑二次幂为指数的素数幂.

囊性纤维变性。基于二次幂分解为n次幂的素数表示.

基于最大素数幂分解的n的表示表

n的最大素数幂分解
127 125 121 113 109 107 103 101 97 89 83 81 79 73 71 67 64 61 59 53 49 47 43 41 37 32 31 29 27 25 23 19 17 16 13 11 9 8 7 5 4 2 基数8
1 0
2 1
1 0
4 1 0 0
5 1 0 0 0
6 1 1
7 1 0 0 0 0
8 1 0 0 0 0 0
9 1 0 0 0 0 0 0
10 1 0 0 1
11 1 0 0 0 0 0 0 0
12 1 1 0
13 1 0 0 0 0 0 0 0 0
14 1 0 0 0 1
15 1 0 1 0
16 1 0 0 0 0 0 0 0 0 0
17 1 0 0 0 0 0 0 0 0 0 0
18 1 0 0 0 0 0 1
19 1 0 0 0 0 0 0 0 0 0 0 0
20 1 1 0 0
21 1 0 0 1 0
22 1 0 0 0 0 0 0 1
23 1 0 0 0 0 0 0 0 0 0 0 0 0
24 1 0 0 0 1 0
25 1 0 0 0 0 0 0 0 0 0 0 0 0 0
26 1 0 0 0 0 0 0 0 1
27 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 1 0 1 0 0
29 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 1 0 1 1
31 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 1 0 0 0 0 0 1 0
34 1 0 0 0 0 0 0 0 0 0 1
35 1 1 0 0 0
36 1 0 0 0 1 0 0
37 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 1 0 0 0 0 0 0 0 0 0 0 1
39 1 0 0 0 0 0 0 1 0
40 1 0 1 0 0 0
41 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
42 1 0 0 1 1
43 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
44 1 0 0 0 0 1 0 0
45 1 0 0 1 0 0 0
46 1 0 0 0 0 0 0 0 0 0 0 0 1
47 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48 1 0 0 0 0 0 0 0 1 0
49 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
50 1 0 0 0 0 0 0 0 0 0 0 0 0 1
51 1 0 0 0 0 0 0 0 0 1 0
52 1 0 0 0 0 0 1 0 0
53 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
54 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
55 1 0 0 0 1 0 0 0
56 1 1 0 0 0 0
57 1 0 0 0 0 0 0 0 0 0 1 0
58 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
59 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
60 1 1 1 0
61 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
62 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
63 1 0 1 0 0 0 0
64 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
65 1 0 0 0 0 1 0 0 0
66 1 0 0 0 0 0 1 1
67 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
68 1 0 0 0 0 0 0 0 1 0 0
69 1 0 0 0 0 0 0 0 0 0 0 1 0
70 1 1 0 0 1
71 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
72 1 1 0 0 0 0 0
73 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
74 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
75 1 0 0 0 0 0 0 0 0 0 0 0 1 0
76 1 0 0 0 0 0 0 0 0 1 0 0
77 1 0 0 1 0 0 0 0
78 1 0 0 0 0 0 0 1 1
79 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
80 1 0 0 0 0 0 1 0 0 0
81 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
82 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
83 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
84 1 0 1 1 0
85 1 0 0 0 0 0 0 1 0 0 0
86 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
87 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
88 1 0 1 0 0 0 0 0
89 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 1 0 0 1 0 0 1
91 1 0 0 0 1 0 0 0 0
92 1 0 0 0 0 0 0 0 0 0 1 0 0
93 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
94 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
95 1 0 0 0 0 0 0 0 1 0 0 0
96 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
97 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
98 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
99 1 1 0 0 0 0 0 0
100 1 0 0 0 0 0 0 0 0 0 0 1 0 0
101 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
102 1 0 0 0 0 0 0 0 0 1 1
103 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
104 1 0 0 1 0 0 0 0 0
105 1 1 0 1 0
106 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
107 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
108 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
109 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
110 1 0 0 0 1 0 0 1
111 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
112 1 0 0 0 0 1 0 0 0 0
113 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
114 1 0 0 0 0 0 0 0 0 0 1 1
115 1 0 0 0 0 0 0 0 0 1 0 0 0
116 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
117 1 0 1 0 0 0 0 0 0
118 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
119 1 0 0 0 0 0 1 0 0 0 0
120 1 0 1 0 1 0
121 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
122 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
123 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
124 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
125 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
126 1 0 1 0 0 0 1
127 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


另请参见