# Happy birthday to me (part 1)

Let $$M/D$$ be the date of my birthday, where $$M$$ and $$D$$ are the month and the day of the date, respectively. Then, there are some properties that relate $$M$$ and $$D$$. They are:

• $$D$$ is divisible by $$M$$;
• $$M$$ represents the number of, not necessarily distinct, prime factors of $$D$$;
• If $$01/01^{st}$$ is a thursday, then $$M/D$$ is a friday.

After applying these properties, you have achieved a few possible dates. These possible dates can be grouped in sets, in function of every possible month, as follows:

$$S({M_i})=\{{D_1}, {D_2}, \ ..., \ {D_n}\}$$.

Then, the last property would be:

• The sum of possible days in a possible month is the smallest as possible.

Find $$M+D$$.

Details and assumptions

• As examples, the number of prime factors of $$8$$ is $$3$$, because $$8=2\cdot{2}\cdot{2}$$, and the number of prime factors of $$20$$ is $$3$$, because $$20=2\cdot{2}\cdot{5}$$
• Assume you are using Gregorian calendar in a non-bissextile year.
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