  In this paper, we study various homology cobordism invariants for Seifert
fibered integral homology 3-spheres derived from Heegaard Floer homology. Our
main tool is lattice homology, a combinatorial invariant defined by
Ozsv\'ath-Szab\'o and N\'emethi. We reprove the fact that the $d$-invariants of
Seifert homology spheres $\Sigma(a_1,a_2,\dots,a_n)$ and
$\Sigma(a_1,a_2,\dots,a_n+a_1a_2\cdots a_{n-1})$ are the same using an explicit
understanding of the behavior of the numerical semigroup minimally generated by
$a_1a_2\cdots a_n/a_i$ for $i\in[1,n]$. We also study the maximal monotone
subroots of the lattice homologies, another homology cobordism invariant
introduced by Dai and Manolescu. We show that the maximal monotone subroots of
the lattice homologies of Seifert homology spheres $\Sigma(a_1,a_2,\dots,a_n)$
and $\Sigma(a_1,a_2,\dots,a_n+2a_1a_2\cdots a_{n-1})$ are the same.
