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:


 * $4, 10, 16, 34, 46, 144, 76, 112, 100, 148, 166, 136, 202, 226, 238, 268, 298, 304, 310, 352, 400, 430, 490, \ldots$

Proof
The technique is to create all sums of $2$ distinct lucky numbers and count the number of times each sum occurs.

To reach the term $46$, for example, is it sufficient to go as high as building the sums up to the lucky number immediately less than $46$.

The sequence of lucky numbers begins:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, \ldots$

and so:

The first $5$ terms of the sequence are seen to appear.