For the smallest number of ICs, ease of 9 V interfacing and ease of use, I don't think much would beat a CD4059
https://www.futurlec.com/4000Series/CD4059.shtml
A microcontroller would much smaller and cheaper, but would need programming and a lot more background knowledge to get it to work, and would need some interface to get to work with 9 V signals.
A third alternative would be to use a couple of 7490 ICs. The 7490 has two dividers, one that divides by 5 and one that divides by 2. You could use the divide by 5 in one of the 7490 ICs to divide by 5, leaving the divide by 3 needed. For the divide by 5, put the input in pin 1, the divided by 5 output will be on pin 11, and pins 2, 3, 6, 7 and 14 need to be grounded.
For the divide by 3, use the second IC divide by 5 input. You then wire the QB and QC outputs up to the R01 and R02 inputs. Then what happens is that the counter resets when it gets to 3, so that it counts 0, 1, 2 and then 3 for a vanishingly short time before going back to 0. You need the input (from the output of the divide by 5) on pin 1, the final divided by 15 output on pin 8, pin 8 also wired to pin 2, pin 9 wired to pin 3, and pins 6, 7 and 14 grounded.
(The 7490 is most often used as a divide by 10, where the first (fastest changing) output is QA. This alternative uses it as a divide by 5, so QA isn't used. The outputs used are QB, QC and QD.)
The 7490 ICs are only available with a 5 V supply.