How many coins supine

For 2006 coins were supine
First flip the coin in order multiples of 1
Last Monday the coin flip sequence is a multiple of 2
Last Tuesday the coin flip sequence is a multiple of 3
4 th flip the coin order is a multiple of 4
...
First flip the coin 2006 order is a multiple of 2006
How many coins supine?
Thank you very much

all but the perfect squares will be supine

each number will have an even number of factors, except the perfect squares, which have an "unmatched factor", or an odd number

an even number of factors means an even number of flips, which returns the coin to its supine position

however, an odd number of factors will leave it in the opposite position

yourself thinking