The phrase "at least a core" is correct and usable in written English.
It can be used when referring to a minimum essential part or component of something, often in a context where additional elements may be present.
Example: "In order to understand the project, you need to grasp at least a core concept of the underlying technology."
Alternatives: "at minimum a core" or "at the very least a core".
At least a core group of very respected professionals".
Or shouldn't all European states share at least a core set of democratic values?
"Many investors would be much better served with a simple 60/40 strategy, or at least a core where you have low-cost index funds.
Loyalty may not be what it once was, but most companies will still be better off with at least a core of people who stay with them across decades.
For the moment, Mr. Gray, whose home base is the village of White Mountain, says his goal is to maintain at least a core of reindeer that can serve as the nucleus for a new industry if and when the caribou population drops.
While these tend to feature a drag-and-drop interface that requires no coding experience, having at least a core competency when it comes to programming will improve your ability to spot and fix bugs within the code, and customize the sites design the way the professionals to.
Instead, buy at least a dual core chip from Intel's Core 2 Duo or AMD's X2 line.
An attempt will be made to collect at least a minimum core length of 1 centimeter on each biopsy core, when possible, in order to allow for a complete analysis.
Your Mac must have at least an Intel Core 2 Duo, Xeon processor, Core i3, Core i5, or Core i7.
There is, first, the internal politics of the Church, where the bishops find themselves, especially on matters of sexuality, increasingly isolated from most Church members; they seem desperate to rally at least a fervid core of supporters around their fading authority.
Dragon Age II needs at least a Intel Core 2 Duo 1.86Ghz or faster chip, Mac OS X 10.6.6 or later, 2GB of RAM or more and a minimum ATI HD2600 or NVidia 9400 or better video card (at least 256MB VRAM).
