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 A055204 Squarefree part of n!: n! divided by its largest square divisor. 18
 1, 2, 6, 6, 30, 5, 35, 70, 70, 7, 77, 231, 3003, 858, 1430, 1430, 24310, 12155, 230945, 46189, 969969, 176358, 4056234, 676039, 676039, 104006, 312018, 44574, 1292646, 1077205, 33393355, 66786710, 2203961430, 64822395, 90751353, 90751353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Smallest number such that n!*a(n) is a square. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..3386 (next term has 1001 digits) Kevin A. Broughan, Asymptotic Order of the Square-free Part of N!, Integers, 2 (2002), Article A.10. Rafael Jakimczuk, On the h-th free part of the factorial, International Mathematical Forum, Vol. 12, 2017, no. 13, 629-634. FORMULA a(n) = A007913(n!) = n!/A055071(n) = A000142(n)/A055071(n). log a(n) ~ n log 2. - Charles R Greathouse IV, Apr 03 2012 sqrt(n!) = A055772(n) * sqrt(a(n)). - Alonso del Arte, Feb 16 2015 EXAMPLE 10! = 518400*7 = 7*(720)^2, so a(10) = 7. MATHEMATICA Table[#/Last@ Select[Divisors@ #, IntegerQ@ Sqrt@ # &] &[n!], {n, 26}] (* Michael De Vlieger, May 02 2016 *) PROG (PARI) a(n)=core(n!) \\ Charles R Greathouse IV, Apr 03 2012 CROSSREFS Cf. A055071, A000142, A007913, A249831. Sequence in context: A130087 A085087 A072983 * A212397 A008339 A077139 Adjacent sequences:  A055201 A055202 A055203 * A055205 A055206 A055207 KEYWORD nonn AUTHOR Labos Elemer, Jun 19 2000 STATUS approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)