Heteroepitaxy on nanopatterned substrates is a means of defect reduction at semiconductor heterointerfaces by exploiting substrate compliance and enhanced elastic lattice relaxation resulting from reduced dimensions. We explore this possibility in the InAs/GaAs(111)A system using a combination of nanosphere lithography and reactive ion etching of the GaAs(111)A substrate for nano-patterning of the substrate, yielding pillars with honeycomb and hexagonal arrangements and varied nearest neighbor distances. Substrate patterning is followed by MBE growth of InAs at temperatures of 150 -350 C and growth rates of 0.011 nm/s and 0.11 nm/s. InAs growth in the form of nano-islands on the pillar tops is achieved by lowering the adatom migration length by choosing a low growth temperature of 150 C at the growth rate 0.011 nm/s. The choice of a higher growth rate of 0.11 nm/s results in higher InAs island nucleation and the formation of hillocks concentrated at the pillar bases due to a further reduction of adatom migration length. A common feature of the growth morphology for all other explored conditions is the formation of merged hillocks or pyramids with well-defined facets due to the presence of a concave surface curvature at the pillar bases acting as adatom sinks.