We present an algorithm, based on the explicit formula for -functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically and use it to prove that several RSA challenge numbers are not squarefull.
Andrew R. Booker. Ghaith A. Hiary. Jon P. Keating. "Detecting squarefree numbers." Duke Math. J. 164 (2) 235 - 275, 1 February 2015. https://doi.org/10.1215/00127094-2856619