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A056839 Squarefree part of lcm(1,...,n). 1
1, 1, 2, 6, 3, 15, 15, 105, 210, 70, 70, 770, 770, 10010, 10010, 10010, 5005, 85085, 85085, 1616615, 1616615, 1616615, 1616615, 37182145, 37182145, 7436429, 7436429, 22309287, 22309287, 646969323, 646969323, 20056049013, 40112098026, 40112098026, 40112098026 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

FORMULA

a(n) = A007913(A003418(n)) = lcm(1..n)/lcm(1..q)^2, where q = floor(sqrt(n)) = A000196(n).

EXAMPLE

n=65: lcm(1..65) = 1182266884102822267511361600, floor(sqrt(65))=8, lcm(1..8) = 8*3*5*7 = 840; a(65) = lcm(1..65)/lcm(1..8)^2 = 1675548305134385299761 is squarefree.

MAPLE

b:= proc(n) b(n):= `if`(n=0, 1, ilcm(b(n-1), n)) end:

a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(b(n))[2]):

seq(a(n), n=0..40);  # Alois P. Heinz, Apr 01 2016

MATHEMATICA

{1}~Join~Array[Sqrt[#] /. (c_: 1) a_^(b_: 0) :> (c a^b)^2 &[LCM @@ Range@ #] &, 34] (* Michael De Vlieger, Oct 26 2017, after Bill Gosper at A007913 *)

PROG

(PARI) a(n) = core(lcm(vector(n, k, k))); \\ Michel Marcus, Oct 27 2017

CROSSREFS

Cf. A007913, A003418, A000196.

Sequence in context: A094299 A304537 A121566 * A302033 A071301 A145642

Adjacent sequences:  A056836 A056837 A056838 * A056840 A056841 A056842

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 29 2000

EXTENSIONS

a(0)=1 inserted by Alois P. Heinz, Apr 01 2016

Edited by Jon E. Schoenfield, Jul 09 2018

STATUS

approved

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Last modified March 25 16:38 EDT 2019. Contains 321474 sequences. (Running on oeis4.)