User blog comment:Simply Beautiful Art/A finite variant to the Madore's OCF./@comment-5529393-20171215040530

A quick check shows that every number less than or equal to 1024 can be represented as a sum of two members of C'(3). (Just find numbers in C'(3) such that each number is within 70 of the last number.)  Combined with the powers of two from 2^10 to 2^26, it follows that every number from 0 to 2^27 can be represented as a sum of at most 19 members of C'(3). Of course, with the remaining 2^27 - 18 summands, we can represent every multiple of 2^27 from 0 to 2^27(2^27 - 18). So every number from 0 to 2^27(2^27 - 17) is a member of C'(4).

On the other hand, most numbers just under 2^27(2^27 + 1) cannot be represented as a sum of 2^27 + 1 numbers in C'(3), and most of them cannot be represented as a product of 2^27 + 1 numbers in C'(3) either. For example, 2^54 + 2^27 - 1 is 11 times a prime, so it is not in C'(4). So psi'(4) is bounded between 2^54 - 17*2^27 + 1 and 2^54 + 2^27 - 1 inclusive.

In general, I would expect that psi'(n+1) is not far below M(n) (M(n) + 1) (I would expect less than M(n)^2, but I haven't proven this.)