CAULK ? auk....aaak....

All manner caulk is available, including some labeled as to paint-compatibility. I'd go for a latex, or butyl-rubber (and wait a week.) J

A latex or siliconized latex should be fine. Heck, you're going to paint over it...it doesn't have to be fancy. However, if you insist on being fancy one of the butyl caulks would also do the trick (pain in the ass to work with, 'tho, and, IMHO, overkill in your situation).

Putty popped out of the holes? Maybe that's the problem someone used putty.

Come on, it is the same as any other regular caulking job on the outside of a house. Use siliconized latex (25 years stuff). It doesn't have to be weather resistant; you are painting over it.

For that I'd go with a paintable latex that cleans up with water but don't do it if there is a chance of rain! :-(

These folks also have some pretty good products, but it's overkill for what you need:

EXTERIOR grade Spackle

Be sure that the 'putty' didn't pop because the nails are pulling out. Use a nail set or a punch and tap on the nails to see if they have worked loose in which case I would pound them home and then install a countersunk screw nest to the nail. Then, caulk over both with one of the aforementioned paintable caulks or exterior spackle (didn't know about that one - 'thanks' to the submitter)

Just remember, whenever you are using caulk, do not flirt with women that walk past your work. There was a painter arrested, because he yelled to a woman walking down the sidewalk

"Hey babe, wanna see my caulk".........

She replied with a definate "NO WAY"

Then he said "Just come on over here babe, and I'll let you stroke my gun"........

Minutes later the painter was arrested !!!!