Several neurodegenerative diseases are associated with the polyglutamine (polyQ) repeat disorder in which a segment of consecutive glutamines in the native protein is produced with too many glutamines. Huntington's disease, for example, is related to the misfolding of the Huntingtin protein which occurs when the polyQ segment has more than approximately 36 glutamines. Experimentally, it is known that the polyQ segment alone aggregates into beta-rich conformations such as amyloid fibrils. Its aggregation is modulated by the number of glutamine residues as well as by the surrounding amino acid sequences such as the 17-amino-acid N-terminal fragment of Huntingtin which increases the aggregation rate. Little structural information is available, however, regarding the first steps of aggregation and the atomistic mechanisms of oligomerization are yet to be described. Following previous coarse-grained replica-exchange molecular dynamics simulations that show the spontaneous formation of a nanotube consisting of two intertwined antiparallel strands (Laghaei, R; Mousseau, N. J. Chem. Phys. 2010, 132, 165102), we study this configuration and some extensions of it using all-atom explicit solvent MD simulations. We compare two different lengths for the polyQ segment, 40 and 30 glutamines, and we investigate the impact of the Huntingtin N-terminal residues (htt(NT)). Our results show that the dimeric nanotubes can provide a building block for the formation of longer nanotubes (hexamers and octamers). These longer nanotubes are characterized by large beta-sheet propensities and a small solvent exposure of the main-chain atoms. Moreover, the oligomerization between two nanotubes occurs through the formation of protein/protein H-bonds and can result in an elongation of the water-filled core. Our results also show that the htt(NT) enhances the structural stability of the beta-rich seeds, suggesting a new mechanism by which it can increase the aggregation rate of the amyloidogenic polyQ sequence.