The inductance of a single loop of wire will increase in inverse proportion to its diameter. Are there exceptions to this rule when applied to multi stranded wire (not litz wire). I should make it clear that the diameter refers to the wire used to form the loop.
For a notionally thin wire, you can say that the magnetic flux produced by any part of the flow of current couples to flux produced by all other parts of the flow of current. This maximizes the wire's inductance.
When the effective cross sectional area of a wire gets larger, current flowing on one edge of the wire can produce a small amount of magnetic flux that does not couple entirely with current flow on the opposite edge. This begins to degrade the overall inductance of the wire.
In an extreme scenario, you could imagine a wire being cut down the centre so that the current splits into two distinct and separate paths. If these two half-wires are at some distance to each other, very little magnetic flux will couple from one half-wire to the other and the net inductance will tend to become 50% of when those two half-wires were united as a whole.
the answer is that when calculating the inductance of a multi stranded wire it is the effective diameter that is relevant to formula.