[seqfan] A093893 Subsequence

[Leroy Quet]

Consider sequence A093893,
This is the list of positive integers n such that the partial sum of any 2 or more divisors of n is composite.

What I wonder about is the subsequence, which doesn't seem to be in the EIS, where the nth term is the smallest term of A093893 with exactly n divisors.

(Starts at a(2).)

3, 49, 87, etc.

It seems that it is very unlikely that this sequence is infinite, or even that it is not short.

Can it be proved that this sequence is finite or infinite?

Thanks,
Leroy Quet