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Summary:
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.
References:
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[2] Heath-Brown D. R.: Review 651.10012. Zentralblatt Mathematik 651, 41 (1989) MR 1441325
[3] Mardjanichvili C.: Estimation d’une somme arithmetique. Dokl. Acad. Sci. SSSR 22 (1939), 387–389. Zbl 0021.20802
[4] Ribenboim P.: Remarks on exponential congruences and powerful numbers. J. Number Theory 29 (1988), 251–263. MR 0955951 | Zbl 0651.10012
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