I am doing a research relatively with anti-divisors and the “opposite” of them numbers .
Actually I am trying to count (to find a formula which counts) the number of pairs*of type (“anti divisor odd composite number less than half of an integer a”---“odd composite number greater than the half of an integer a”) such as the addition of them has as result the integer a.
For example :24=9+15
9<24/2 is odd comp. and does not divide 24
and 24>15>24/2 is and odd comp.
So there is one pair * of integers of the this specific type for the number 24...
I have done some work on that but I didn’t yet found one way to count exactly the number of ways which an integer can be written on this way.
the only thing I know about that is a lower bound for this number but its not really useful.I t would be more useful to know the upper bound value
Does anyone knows anything about that?