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unitary_powerfree_sigma.sf

unitary_powerfree_sigma.sf 2.2 KB
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  1. #!/usr/bin/ruby
    2. 

  2. 

  3. # Sum of the unitary k-powerfree divisors of n.
    4. 

  4. 

  5. # See also:
    6. 

  6. #   https://oeis.org/A092261
    7. 

  7. 

  8. func unitary_powerfree_sigma(n, k=2, j=1) {
    9. 

  9. 

  10.     var prod = 1
    11. 

  11. 

  12.     for p,e in (n.factor_exp) {
    13. 

  13.         e < k || next
    14. 

  14.         #prod *= usigma(p**e, j)
    15. 

  15.         prod *= (p**(e*j) + 1)
    16. 

  16.     }
    17. 

  17. 

  18.     return prod
    19. 

  19. }
    20. 

  20. 

  21. for n in (1..20) {
    22. 

  22.     say "sum of unitary squarefree divisors of #{n} is #{unitary_powerfree_sigma(n, 2)}"
    23. 

  23. 

  24.     assert_eq(unitary_powerfree_sigma(n, 2), n.udivisors.grep { .is_powerfree(2) }.sum)
    25. 

  25.     assert_eq(unitary_powerfree_sigma(n, 3), n.udivisors.grep { .is_powerfree(3) }.sum)
    26. 

  26.     assert_eq(unitary_powerfree_sigma(n, 4), n.udivisors.grep { .is_powerfree(4) }.sum)
    27. 

  27. 

  28.     assert_eq(unitary_powerfree_sigma(n, 2, 2), n.udivisors.grep { .is_powerfree(2) }.sum { _**2 })
    29. 

  29.     assert_eq(unitary_powerfree_sigma(n, 3, 2), n.udivisors.grep { .is_powerfree(3) }.sum { _**2 })
    30. 

  30.     assert_eq(unitary_powerfree_sigma(n, 4, 2), n.udivisors.grep { .is_powerfree(4) }.sum { _**2 })
    31. 

  31. 

  32.     assert_eq(unitary_powerfree_sigma(n, 2, 3), n.udivisors.grep { .is_powerfree(2) }.sum { _**3 })
    33. 

  33.     assert_eq(unitary_powerfree_sigma(n, 3, 3), n.udivisors.grep { .is_powerfree(3) }.sum { _**3 })
    34. 

  34.     assert_eq(unitary_powerfree_sigma(n, 4, 3), n.udivisors.grep { .is_powerfree(4) }.sum { _**3 })
    35. 

  35. }
    36. 

  36. 

  37. __END__
    38. 

  38. sum of unitary squarefree divisors of 1 is 1
    39. 

  39. sum of unitary squarefree divisors of 2 is 3
    40. 

  40. sum of unitary squarefree divisors of 3 is 4
    41. 

  41. sum of unitary squarefree divisors of 4 is 1
    42. 

  42. sum of unitary squarefree divisors of 5 is 6
    43. 

  43. sum of unitary squarefree divisors of 6 is 12
    44. 

  44. sum of unitary squarefree divisors of 7 is 8
    45. 

  45. sum of unitary squarefree divisors of 8 is 1
    46. 

  46. sum of unitary squarefree divisors of 9 is 1
    47. 

  47. sum of unitary squarefree divisors of 10 is 18
    48. 

  48. sum of unitary squarefree divisors of 11 is 12
    49. 

  49. sum of unitary squarefree divisors of 12 is 4
    50. 

  50. sum of unitary squarefree divisors of 13 is 14
    51. 

  51. sum of unitary squarefree divisors of 14 is 24
    52. 

  52. sum of unitary squarefree divisors of 15 is 24
    53. 

  53. sum of unitary squarefree divisors of 16 is 1
    54. 

  54. sum of unitary squarefree divisors of 17 is 18
    55. 

  55. sum of unitary squarefree divisors of 18 is 3
    56. 

  56. sum of unitary squarefree divisors of 19 is 20
    57. 

  57. sum of unitary squarefree divisors of 20 is 6
    58. 

  58.