Statistics

Problem Statement for "ProperDivisors"

Problem Statement

An integer k greater than 0 is called a cool divisor of m if it is less than m and divides m, but k^n does not divide m. Let d(m) denote the number of cool divisors that exist for an integer m. Given two integers a and b return the sum d(a) + d(a + 1) + ... + d(a + b).

Definition

Class:
ProperDivisors
Method:
analyzeInterval
Parameters:
int, int, int
Returns:
int
Method signature:
int analyzeInterval(int a, int b, int n)
(be sure your method is public)

Notes

  • The result will always fit into a signed 32-bit integer.

Constraints

  • a will be between 1 and 1000000 (10^6), inclusive.
  • b will be between 1 and 10000000 (10^7), inclusive.
  • n will be between 2 and 10, inclusive.

Examples

  1. 32

    1

    3

    Returns: 5

    The cool divisors of 32 are 4, 8 and 16 so d(32) = 3; the cool divisors of 33 are 3 and 11 so d(33) = 2. Hence the desired sum d(32) + d(33) = 3 + 2 = 5.

  2. 1

    12

    2

    Returns: 8

  3. 1000000

    10000000

    10

    Returns: 146066338

  4. 1000000

    10000000

    5

    Returns: 145707011

  5. 1

    1

    10

    Returns: 0

  6. 1000000

    10000000

    2

    Returns: 139630317

  7. 256

    1

    8

    Returns: 6

  8. 76

    241

    7

    Returns: 1051

  9. 25

    481

    5

    Returns: 2171

  10. 77

    237

    2

    Returns: 897

  11. 80

    528

    5

    Returns: 2559

  12. 95

    801

    4

    Returns: 4121

  13. 33

    460

    5

    Returns: 2077

  14. 68

    188

    3

    Returns: 757

  15. 18

    46

    2

    Returns: 108

  16. 2

    655

    4

    Returns: 3000

  17. 13

    930

    2

    Returns: 4147

  18. 18

    23

    7

    Returns: 60

  19. 33

    645

    5

    Returns: 3095

  20. 56

    34

    9

    Returns: 124

  21. 32

    697

    8

    Returns: 3414

  22. 60

    40

    3

    Returns: 144

  23. 23

    227

    5

    Returns: 883

  24. 4

    492

    6

    Returns: 2166

  25. 8

    706

    10

    Returns: 3378

  26. 95

    744

    10

    Returns: 3839

  27. 16

    217

    3

    Returns: 785

  28. 33

    669

    9

    Returns: 3258

  29. 2063

    31790

    6

    Returns: 278126

  30. 136

    33591

    10

    Returns: 288948

  31. 9715

    57300

    4

    Returns: 545073

  32. 2123

    89026

    2

    Returns: 803335

  33. 3772

    17425

    2

    Returns: 136822

  34. 4565

    79739

    10

    Returns: 770484

  35. 4854

    37177

    8

    Returns: 337520

  36. 6293

    33607

    2

    Returns: 284179

  37. 2612

    79478

    3

    Returns: 745659

  38. 7376

    29801

    5

    Returns: 269443

  39. 8342

    97317

    6

    Returns: 965666

  40. 8452

    90781

    8

    Returns: 897383

  41. 2915

    49955

    6

    Returns: 458682

  42. 6631

    44593

    10

    Returns: 414791

  43. 7520

    20703

    3

    Returns: 179741

  44. 5453

    44995

    5

    Returns: 414695

  45. 4715

    73754

    10

    Returns: 708291

  46. 6409

    36882

    5

    Returns: 336559

  47. 7303

    87584

    10

    Returns: 860793

  48. 9534

    54527

    5

    Returns: 519000

  49. 282499

    2413

    10

    Returns: 28239

  50. 570551

    5440141

    7

    Returns: 76173349

  51. 818936

    1919226

    4

    Returns: 25736733

  52. 542079

    3570232

    7

    Returns: 48852298

  53. 43959

    9287861

    2

    Returns: 126168618

  54. 896415

    7577294

    3

    Returns: 107374885

  55. 618745

    4921657

    2

    Returns: 65522750

  56. 297360

    954291

    3

    Returns: 11871712

  57. 698735

    9276167

    10

    Returns: 134219467

  58. 438626

    2729469

    7

    Returns: 36663471

  59. 506878

    2729424

    5

    Returns: 36715498

  60. 566290

    898966

    7

    Returns: 11634824

  61. 227177

    7901290

    8

    Returns: 111914619

  62. 352823

    4804748

    2

    Returns: 63244619

  63. 406067

    449339

    4

    Returns: 5573981

  64. 60173

    8645346

    9

    Returns: 122474390

  65. 549084

    9278832

    7

    Returns: 133777741

  66. 429413

    806914

    8

    Returns: 10280643

  67. 100368

    9604230

    4

    Returns: 136456858

  68. 944525

    9999760

    7

    Returns: 145854621

  69. 904376

    9999520

    5

    Returns: 145466065

  70. 959824

    9999764

    2

    Returns: 139529868

  71. 909621

    9999473

    5

    Returns: 145478423

  72. 973806

    9999200

    4

    Returns: 145177767

  73. 980468

    9999541

    5

    Returns: 145653011

  74. 904433

    9999813

    3

    Returns: 143819454

  75. 928883

    9999955

    2

    Returns: 139456772

  76. 912999

    9999346

    4

    Returns: 145030855

  77. 921788

    9999071

    2

    Returns: 139426278

  78. 1

    10000000

    2

    Returns: 136280624

  79. 1

    10000000

    5

    Returns: 142356103

  80. 1

    10000000

    8

    Returns: 142684598

  81. 537695

    5376956

    5

    Returns: 75009840

  82. 100000

    10000000

    10

    Returns: 143276440

  83. 97

    9999999

    3

    Returns: 140706252

  84. 1

    10000000

    7

    Returns: 142641878

  85. 1

    10000000

    10

    Returns: 142715423

  86. 999999

    9999990

    9

    Returns: 146056082

  87. 99999

    999999

    7

    Returns: 12296705

  88. 787878

    10000000

    3

    Returns: 143524980

  89. 2

    10000000

    6

    Returns: 142551958

  90. 1000000

    9999999

    9

    Returns: 146056106

  91. 999951

    9188771

    9

    Returns: 133621562

  92. 934234

    9123756

    9

    Returns: 132473466

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