We show that $n^2+1$ is powerfull for $O(x^{2/5+\epsilon })$ integers $n\le x$ at most, thus answering a question of P. Ribenboim.
@article{107865,
author = {Jan-Christoph Puchta},
title = {On the powerful part of $n\sp 2+1$},
journal = {Archivum Mathematicum},
volume = {039},
year = {2003},
pages = {187-189},
zbl = {1122.11311},
mrnumber = {2010719},
language = {en},
url = {http://dml.mathdoc.fr/item/107865}
}
Puchta, Jan-Christoph. On the powerful part of $n\sp 2+1$. Archivum Mathematicum, Tome 039 (2003) pp. 187-189. http://gdmltest.u-ga.fr/item/107865/
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