I figured out a way that is almost as good. Early on in Google sheets double clicking the paintbrush icon worked. Why Google removed that I don't know. But while you can't make the paintbrush icon "stick" anymore, what you can do is:

1. click the cell (or range of cells) whose format you want to copy.
2. click the paint-format paintbrush icon (to copy format).
3. click the first cell you want to copy that format to. That cell will receive the copied format.
4. click the next cell (or range of cells) you want that same format copied to. Use ctrl-click to select multiple non-adjacent cells. Can select non-adjacent cells only if you selected just 1 cell in step 1.
5. press CTRL-Y (to re-do the paste-format). That cell will receive the same format you originally copied in steps 1/2 above).
6. Repeat 4/5 above for all cells that you want the format copied to.

you can use this: CTRL + ALT + V

To add to the Bob Jones explanation of the Format Painter button:

If you select a cell whose format you want to copy and then double-click the Format Painter button, you get "sticky" behavior instead of the "one shot deal."

After you double-click the Format Painter button, to apply the previously selected format, you can click and click-and-drag to select non-adjacent cells and ranges.

Then turn off the "sticky" behavior by clicking the Format Painter button.