This solution seems like it would benefit from factoring out some code, just for clarity, even if it's not reused, and possibly from making multiple passes over the input ( which does not affect Big-O complexity ).

gotcha.

...because that would have been an incorrect formula.

Test failed with month = 1: 0 should equal 1
Test failed with month = 7: 2 should equal 3
Test Passed
Test Passed
Test Passed
Test failed with month = 4: 1 should equal 2
Test failed with month = 2: 0 should equal 1
Test failed with month = 10: 3 should equal 4
Test failed with month = 11: 3 should equal 4
Test failed with month = 8: 2 should equal 3
Test Passed
Test failed with month = 5: 1 should equal 2

Oh sorry, I overlooked the instructions, and I don't know why it's tagged "issue", it was meant to be just a suggestion

2.00 is a float to the computer, but 2.00 == 2 returns true. if you want to check the type of the variable, I think it would make more sense to say "if the value passed is of the type integer", not "if the value is an integer", and remove the tag "mathematics"

Not an issue, maybe a suggestion, but it's stated in the instructions:

Your output cannot end with a newline.

The Kata could ignore a last line break, as many users will probably do this and get frustrated when it doesn't work

2.00 is a float, not an integer

Mathematically speaking, 2.00 is an integer, but the test case says otherwise

Considering computers need to check if a number is greater then another to do sorting, it's right now impossible to have a "No Loop Sorting Array", that would be an algorithm O(1), and such an algorithm doesn't nor will exist in regular computers