Weird and Semi-perfect numbers

[abhinav-anand-addepar]

• ntheory
  • Added new functions to implement semi-perfect numbers and weird numbers

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• ntheory
  • Added new functions to implement semi-perfect numbers and weird numbers (#18128 by @abhinav28071999)

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 <!-- BEGIN RELEASE NOTES -->
* ntheory
  *  Added new functions to implement semi-perfect numbers and weird numbers
<!-- END RELEASE NOTES -->

[ethankward]

For the numbers 66, 78, 102, 114, 138... your algorithm returns False, but these are semiperfect numbers.

[abhinav-anand-addepar]

@ethankward I have made the required changes.

[ethankward]

Why are you using this complicated algorithm instead of just using itertools.combinations?

[codecov]

Codecov Report

Merging #18128 into master will increase coverage by 6.202%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##            master    #18128       +/-   ##
=============================================
+ Coverage   68.733%   74.935%   +6.202%     
=============================================
  Files          642       642               
  Lines       166965    166991       +26     
  Branches     39281     39291       +10     
=============================================
+ Hits        114761    125136    +10375     
+ Misses       46657     36316    -10341     
+ Partials      5547      5539        -8

[czgdp1807]

What about symbolic inputs?

>>> is_semiperfect(n)
Traceback (most recent call last):
  File "/home/czgdp1807/sympy_project/sympy/sympy/core/compatibility.py", line 419, in as_int
    raise TypeError
TypeError

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/usr/lib/python3.6/code.py", line 91, in runcode
    exec(code, self.locals)
  File "<console>", line 1, in <module>
  File "/home/czgdp1807/sympy_project/sympy/sympy/ntheory/factor_.py", line 2394, in is_semiperfect
    factors = divisors(n)
  File "/home/czgdp1807/sympy_project/sympy/sympy/ntheory/factor_.py", line 1438, in divisors
    n = as_int(abs(n))
  File "/home/czgdp1807/sympy_project/sympy/sympy/core/compatibility.py", line 425, in as_int
    raise ValueError('%s is not an integer' % (n,))
ValueError: Abs(n) is not an integer
>>> 

[czgdp1807]

@abhinav28071999 Please resolve conflicts in this PR.

[czgdp1807]

It can be transformed to a one liner, return is_abundant(n) == True and is_semiperfect(n) == False.
IMO, this function simply uses two pre-defined functions without much manipulations, so we can remove is_weird.

[czgdp1807]

@abhinav28071999 Would you still like to work on this?

[abhinav-anand-addepar]

I will pass on this one. I will put a takeover label.