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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