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A056059 GCD of largest square and squarefree part of central binomial coefficients. 9
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 6, 2, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 6, 3, 1, 1, 1, 2, 3, 6, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 3, 6, 6, 3, 1, 2, 2, 1, 2, 1, 3, 6, 1, 1, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A055229(A001405(n)), where A055229(n) = gcd(A008833(n), A007913(n)).

EXAMPLE

n=14, binomial(14,7) = 3432 = 8*3*11*13. The largest square divisor is 4, squarefree part is 858. So a(14) = gcd(4,858) = 2.

MATHEMATICA

Table[GCD[First@ Select[Reverse@ Divisors@ #, IntegerQ@ Sqrt@ # &], Times @@ Power @@@ Map[{#1, Mod[#2, 2]} & @@ # &, FactorInteger@ #]] &@ Binomial[n, Floor[n/2]], {n, 80}] (* Michael De Vlieger, Feb 18 2017, after Zak Seidov at A007913 *)

PROG

(PARI)

A001405(n) = binomial(n, n\2);

A055229(n) = { my(c=core(n)); gcd(c, n/c); } \\ Charles R Greathouse IV, Nov 20 2012

A056059(n) = A055229(A001405(n)); \\ Antti Karttunen, Jul 20 2017

(Python)

from sympy import binomial, gcd, floor

from sympy.ntheory.factor_ import core

def a001405(n): return binomial(n, floor(n/2))

def a055229(n):

    c=core(n)

    return gcd(c, n/c)

def a(n): return a055229(a001405(n))

print map(a, range(1, 151)) # Indranil Ghosh, Jul 20 2017

CROSSREFS

Cf. A000188, A001405, A007913, A008833, A034974, A046098, A055229, A055231.

Cf. A056056, A056057, A056058, A056060, A056061.

Sequence in context: A238015 A257679 A031214 * A158819 A031279 A124778

Adjacent sequences:  A056056 A056057 A056058 * A056060 A056061 A056062

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 26 2000

EXTENSIONS

Formula clarified by Antti Karttunen, Jul 20 2017

STATUS

approved

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Last modified February 23 16:14 EST 2020. Contains 332173 sequences. (Running on oeis4.)