Get an anvil and books for Looting and Silk Touch (any level). Put Looting in the left slot and Silk Touch in the right slot. Take a peek at the resulting book to verify that they will combine. Now swap the two books so Silk Touch is in the left slot and Looting is in the right slot. The resulting book will be only Silk Touch. The same happens when you substitute Luck of the Sea for Looting. Fortune won't combine either way.

Not that there's really any point to this, but it's a remarkable inconsistency. It stems from the way Silk Touch and Fortune are prevented from combining. I can see you'd block that combination because Silk Touch would preempt Fortune anyway. But it isn't implemented correctly. Fortune, Looting, and Luck of the Sea are all represented by the same class. If you ask that class whether it will combine with Silk Touch, it refuses regardless of which of the three enchantments it represents. If you ask Silk Touch, it only refuses if the other enchantment is Fortune specifically.

I'm calling to allow Silk Touch + Looting/LoTS, not disallow Looting/LoTS + Silk Touch. This is to be consistent with all other enchantments that are incompatible by virtue of applying to different sets of tools, which simply combine. Enchanting tables also naturally produce combinations like Smite + Protection (or, indeed, potentially Looting + Silk Touch) on books. This apparent impossibility is resolved when the book is applied to an item (sword only getting Smite or armor only getting Protection). I'm not too fond of this forced disposal of costly enchantments, but consistency is paramount. Alternatively, you could block all nonsensical combinations, not just these two.