how many integers from 1 to 2009 are divisible by 5, or by 7, or by 9?

Question

anonymous · Answer

is there an equation to find this out or do we just have to find out this?

anonymous · Answer

I got 785 by brute force.

Table[
  {! Mod[n, 5] == 0 && ! Mod[n, 7] == 0 && ! Mod[n, 9] == 0}, {n, 2009}
  ] // Flatten

The preceding Mathematica statement produces a list of the words True and False, 2009 words in length.  True means that neither 5, 7 or 9 divide n and False means that at least one of the thee divides n.

The list was pasted into EditPadPro where it was instructed to count the number of "False" words.