Smallest Sum of 2 Lucky Numbers in n Ways

Sequence
The sequence of positive integers which can be expressed as the sum of $2$ distinct lucky numbers in $n$ different ways begins:


 * $4, 10, 16, 34, \ldots$

This sequence appears not to be covered on.

Proof
The sequence of lucky numbers begins:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, \ldots$

...etc.