Geodesic
ON THE SQUARE-FREE PARTS OF ⌊en!⌋
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 391-403

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DOI

In this note, we show that if we write ⌊en!⌋ = s(n)u(n)2, where s(n) is square-free then has at least C log log N distinct prime factors for some absolute constant C > 0 and sufficiently large N. A similar result is obtained for the total number of distinct primes dividing the mth power-free part of s(n) as n ranges from 1 to N, where m ≥ 3 is a positive integer. As an application of such results, we give an upper bound on the number of n ≤ N such that ⌊en!⌋ is a square.
DOI : 10.1017/S0017089507003734
Mots-clés : 11B83, 11D41, 11N36 
LUCA, FLORIAN; SHPARLINSKI, IGOR E. ON THE SQUARE-FREE PARTS OF ⌊en!⌋. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 391-403. doi: 10.1017/S0017089507003734
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     journal = {Glasgow mathematical journal},
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     year = {2007},
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