Función: Función DivisorVolver

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…

divisores