[seqfan] sum of divisors and integer partitions

[Joerg Arndt]

Regarding some seqs about various sums over divisors:
 A000203 (all divs)
 A000593 (odd divs)
 A048250 (square-free divs)
 A034448 (unitary divs)
 A048146 (non-unitary divs)
 A162296 (square-full divs)

Are any of the formulas (given at p.347-348 of the fxtbook) connecting
these to certain generating for integer partitions functions new?
(fxtbook URL is  http://www.jjj.de/fxt/#fxtbook ).

I am asking because I never toyed around with sum-of-divs functions.