I am onion!

Cody has 4 types of onions.

\(\bullet\) The number of \(\color{Purple}\text{purple}\) onions can be any non-negative integer.

\(\bullet\) The number of \(\color{Green}\text{green}\) onions is a multiple of 2.

\(\bullet\) The number of \(\color{Red}\text{red}\) onions is a multiple of 3.

\(\bullet\) The number of \(\color{Blue}\text{blue}\) onions is a multiple of 5.

If Cody has 23 onions, how many different distributions of colors can there be?

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