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This is an interesting question. From B. Rosser, Extensions of some theorems of Gödel and Church:

Corollary I. If a class can be enumerated (allowing repetitions) by a general recursive function, it can be enumerated (allowing repetitions) by a primitive recursive function.

Hence any complete recursively enumerable set (such as $K$) K) should work.

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This is an interesting question. From B. Rosser, Extensions of some theorems of Gödel and Church:

Corollary I. If a class can be enumerated (allowing repetitions) by a general recursive function, it can be enumerated (allowing repetitions) by a primitive recursive function.

Hence any complete recursively enumerable set (such as $K$) should work.