From the photo I have no idea if that is a C-7 1/2 or a C-9 but here is a page of C-9 for you
Super Bright Leds CompanyI suspect they have C-7 as well..
The number refers to both the size of the base and the wattage *IF* they are used as a standard christmas tree lamp. the C-7 50 years ago was the most common INDOOR before the mini-lamps became popular. This type of string each lamp is independent, if one goes out, one goes out (The mini's if one goes out they all go out).
The C-9 was the larger outdoor lamp
Both bases today can be found in assorted wattages,, Very assorted wattages with the C-7 base being the most popular.
And you can get an adapter to turn a C-9 or an Edison (Standard lamp socket) into a C-7 if you need one.