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A055204 Squarefree part of n!: n! divided by its largest square divisor. 16
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)

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 July 22 03:22 EDT 2017. Contains 289648 sequences.