Descripción
Función divisorhttps://es.wikipedia.org/wiki/Funci%C3%B3n_divisor
Cadena de entrada
fdiv
Cadena de salida
fdiv
Uso
fdiv(<entero>[,<exp>])
Parámetros | |||
---|---|---|---|
# | Parámetro | Descripción | Valor por defecto |
1 | entero | Entero a aplicar la función divisor | |
2 | exp | Exponente a elevar cada divisor.
Si el valor es 0 o no se especifica este parámetro y <entero> es EnteroGrande, se obtiene la función tau, que devuelve el nº de divisores Si el valor es 1 o no se especifica este parámetro y <entero> es RealDoble, se obtiene la función sigma, que devuelve la suma de divisores |
0|1 |
Ejemplos
nº de divisores, función tau τ=σ0:
fdiv(10b)
RealDoble: 4
fdiv(10b)=dim(div(10))
Booleano: verdadero
suma de divisores, función sigma σ=σ1:
fdiv(10)
RealDoble: 18
fdiv(10)=sum(div(10))
Booleano: verdadero
σ2:
fdiv(10,2)
RealDoble: 130
fdiv(10,-1)
RealDoble: 1.8
tabla HTML usando la exportación HTML del modo REPL de JME:
export html jme=sucesion([div(n)];;sucesion(fdiv(n,x),x,0,3),n,1,100) salto=si nums=si encabezados="n","divisores","sigma1","sigma2","sigma3","sigma4"
Salida JME/REPL:
n | divisores | sigma1 | sigma2 | sigma3 | sigma4 |
---|---|---|---|---|---|
1 | [1] | 1 | 1 | 1 | 1 |
2 | [1,2] | 2 | 3 | 5 | 9 |
3 | [1,3] | 2 | 4 | 10 | 28 |
4 | [1,2,4] | 3 | 7 | 21 | 73 |
5 | [1,5] | 2 | 6 | 26 | 126 |
6 | [1,2,3,6] | 4 | 12 | 50 | 252 |
7 | [1,7] | 2 | 8 | 50 | 344 |
8 | [1,2,4,8] | 4 | 15 | 85 | 585 |
9 | [1,3,9] | 3 | 13 | 91 | 757 |
10 | [1,2,5,10] | 4 | 18 | 130 | 1134 |
11 | [1,11] | 2 | 12 | 122 | 1332 |
12 | [1,2,3,4,6,12] | 6 | 28 | 210 | 2044 |
13 | [1,13] | 2 | 14 | 170 | 2198 |
14 | [1,2,7,14] | 4 | 24 | 250 | 3096 |
15 | [1,3,5,15] | 4 | 24 | 260 | 3528 |
16 | [1,2,4,8,16] | 5 | 31 | 341 | 4681 |
17 | [1,17] | 2 | 18 | 290 | 4914 |
18 | [1,2,3,6,9,18] | 6 | 39 | 455 | 6813 |
19 | [1,19] | 2 | 20 | 362 | 6860 |
20 | [1,2,4,5,10,20] | 6 | 42 | 546 | 9198 |
21 | [1,3,7,21] | 4 | 32 | 500 | 9632 |
22 | [1,2,11,22] | 4 | 36 | 610 | 11988 |
23 | [1,23] | 2 | 24 | 530 | 12168 |
24 | [1,2,3,4,6,8,12,24] | 8 | 60 | 850 | 16380 |
25 | [1,5,25] | 3 | 31 | 651 | 15751 |
26 | [1,2,13,26] | 4 | 42 | 850 | 19782 |
27 | [1,3,9,27] | 4 | 40 | 820 | 20440 |
28 | [1,2,4,7,14,28] | 6 | 56 | 1050 | 25112 |
29 | [1,29] | 2 | 30 | 842 | 24390 |
30 | [1,2,3,5,6,10,15,30] | 8 | 72 | 1300 | 31752 |
31 | [1,31] | 2 | 32 | 962 | 29792 |
32 | [1,2,4,8,16,32] | 6 | 63 | 1365 | 37449 |
33 | [1,3,11,33] | 4 | 48 | 1220 | 37296 |
34 | [1,2,17,34] | 4 | 54 | 1450 | 44226 |
35 | [1,5,7,35] | 4 | 48 | 1300 | 43344 |
36 | [1,2,3,4,6,9,12,18,36] | 9 | 91 | 1911 | 55261 |
37 | [1,37] | 2 | 38 | 1370 | 50654 |
38 | [1,2,19,38] | 4 | 60 | 1810 | 61740 |
39 | [1,3,13,39] | 4 | 56 | 1700 | 61544 |
40 | [1,2,4,5,8,10,20,40] | 8 | 90 | 2210 | 73710 |
41 | [1,41] | 2 | 42 | 1682 | 68922 |
42 | [1,2,3,6,7,14,21,42] | 8 | 96 | 2500 | 86688 |
43 | [1,43] | 2 | 44 | 1850 | 79508 |
44 | [1,2,4,11,22,44] | 6 | 84 | 2562 | 97236 |
45 | [1,3,5,9,15,45] | 6 | 78 | 2366 | 95382 |
46 | [1,2,23,46] | 4 | 72 | 2650 | 109512 |
47 | [1,47] | 2 | 48 | 2210 | 103824 |
48 | [1,2,3,4,6,8,12,16,24,48] | 10 | 124 | 3410 | 131068 |
49 | [1,7,49] | 3 | 57 | 2451 | 117993 |
50 | [1,2,5,10,25,50] | 6 | 93 | 3255 | 141759 |
51 | [1,3,17,51] | 4 | 72 | 2900 | 137592 |
52 | [1,2,4,13,26,52] | 6 | 98 | 3570 | 160454 |
53 | [1,53] | 2 | 54 | 2810 | 148878 |
54 | [1,2,3,6,9,18,27,54] | 8 | 120 | 4100 | 183960 |
55 | [1,5,11,55] | 4 | 72 | 3172 | 167832 |
56 | [1,2,4,7,8,14,28,56] | 8 | 120 | 4250 | 201240 |
57 | [1,3,19,57] | 4 | 80 | 3620 | 192080 |
58 | [1,2,29,58] | 4 | 90 | 4210 | 219510 |
59 | [1,59] | 2 | 60 | 3482 | 205380 |
60 | [1,2,3,4,5,6,10,12,15,20,30,60] | 12 | 168 | 5460 | 257544 |
61 | [1,61] | 2 | 62 | 3722 | 226982 |
62 | [1,2,31,62] | 4 | 96 | 4810 | 268128 |
63 | [1,3,7,9,21,63] | 6 | 104 | 4550 | 260408 |
64 | [1,2,4,8,16,32,64] | 7 | 127 | 5461 | 299593 |
65 | [1,5,13,65] | 4 | 84 | 4420 | 276948 |
66 | [1,2,3,6,11,22,33,66] | 8 | 144 | 6100 | 335664 |
67 | [1,67] | 2 | 68 | 4490 | 300764 |
68 | [1,2,4,17,34,68] | 6 | 126 | 6090 | 358722 |
69 | [1,3,23,69] | 4 | 96 | 5300 | 340704 |
70 | [1,2,5,7,10,14,35,70] | 8 | 144 | 6500 | 390096 |
71 | [1,71] | 2 | 72 | 5042 | 357912 |
72 | [1,2,3,4,6,8,9,12,18,24,36,72] | 12 | 195 | 7735 | 442845 |
73 | [1,73] | 2 | 74 | 5330 | 389018 |
74 | [1,2,37,74] | 4 | 114 | 6850 | 455886 |
75 | [1,3,5,15,25,75] | 6 | 124 | 6510 | 441028 |
76 | [1,2,4,19,38,76] | 6 | 140 | 7602 | 500780 |
77 | [1,7,11,77] | 4 | 96 | 6100 | 458208 |
78 | [1,2,3,6,13,26,39,78] | 8 | 168 | 8500 | 553896 |
79 | [1,79] | 2 | 80 | 6242 | 493040 |
80 | [1,2,4,5,8,10,16,20,40,80] | 10 | 186 | 8866 | 589806 |
81 | [1,3,9,27,81] | 5 | 121 | 7381 | 551881 |
82 | [1,2,41,82] | 4 | 126 | 8410 | 620298 |
83 | [1,83] | 2 | 84 | 6890 | 571788 |
84 | [1,2,3,4,6,7,12,14,21,28,42,84] | 12 | 224 | 10500 | 703136 |
85 | [1,5,17,85] | 4 | 108 | 7540 | 619164 |
86 | [1,2,43,86] | 4 | 132 | 9250 | 715572 |
87 | [1,3,29,87] | 4 | 120 | 8420 | 682920 |
88 | [1,2,4,8,11,22,44,88] | 8 | 180 | 10370 | 779220 |
89 | [1,89] | 2 | 90 | 7922 | 704970 |
90 | [1,2,3,5,6,9,10,15,18,30,45,90] | 12 | 234 | 11830 | 858438 |
91 | [1,7,13,91] | 4 | 112 | 8500 | 756112 |
92 | [1,2,4,23,46,92] | 6 | 168 | 11130 | 888264 |
93 | [1,3,31,93] | 4 | 128 | 9620 | 834176 |
94 | [1,2,47,94] | 4 | 144 | 11050 | 934416 |
95 | [1,5,19,95] | 4 | 120 | 9412 | 864360 |
96 | [1,2,3,4,6,8,12,16,24,32,48,96] | 12 | 252 | 13650 | 1048572 |
97 | [1,97] | 2 | 98 | 9410 | 912674 |
98 | [1,2,7,14,49,98] | 6 | 171 | 12255 | 1061937 |
99 | [1,3,9,11,33,99] | 6 | 156 | 11102 | 1008324 |
100 | [1,2,4,5,10,20,25,50,100] | 9 | 217 | 13671 | 1149823 |
Véase también…