Looks like the Improved Mauser Model Es 340 (1924)
The "Es" probably stood for Einzenschuss German for single shot.
Mauser had stiff competition, with companies like Anschutz, Haenel and GECO.
Mauser company, started making this model in 1924, and stopped making this particular model in 1929. Your appears to be fairly early production as this model series started at 20### (1924) & ended in 80### (late 1929) The next model was designated Es 340 N (New model) and started production in mid-1930. As the world's economy went for cr@p in and around 1924, more & more Germans were joining shooting clubs. These new shooters demanded better rifles with better target rifle features IE-heavier barrels and better triggers. Mauser chose to improve on thier first three model the Eb 300,En 310 and En 320, all single shot rifles in 22 LR.
To confirm this is a Model 340, the action measurements are: action 4.65 long by .94 inches wide. Action flat on bottom, machined trigger guard, smooth finish on early models, knurled on later versions. Same with the finger groove on the forestock, not seen on early ones, present on later models. The Mauser banner seen on the butt plate went from steel to horn to black plastic material.
The sliding safety was first seen on the Es 340, barrel is 25 inches long,sights from 30-200 meters soldered onto barrel. Gas vents not present on early ones, but present on later ones on the LH side of the action ring. Weight of 6 1/2 pounds.
The 340 became one of the most popular Mauser target rifles seen on German ranges.
German patent stamps "D.R.P. D.R.G.M." did not appear until serial # range 50,000 and higher.
This rifle may have come to North America via two routes, first with distributors such as Stoeger Co. of New York circa 1924, or perhaps more likely, in the duffle-bag of a returning victorious Allied soldier Post-WW2. Oh, I forgot, even the South Africans imported these smallbore Mausers too, so who knows?
(Myself I have a later made, Es 350b Championship rifle & I like these old German smallbores very much)
Edit: This information gleaned fron Jon Speed's book entitled "Mauser Smallbores, Sporting, Target & Training Rifles."
PS: The serial number range is hard to pin down to exact year of manufacture, with these incomplete records.
Value is kind of hit or miss here in Canada. What could easily bring 600-700 dollars in the US market, might draw less of a crowd in our maple leaf country. IF one could find an interested buyer & my quoted dollar value may seem a little too low, but one could wait a while to off-load it as well!! (helpful aren't I ?!?!)