A057815 - OEIS

A057815

a(n) = gcd(n,binomial(n,floor(n/2))).

1, 2, 3, 2, 5, 2, 7, 2, 9, 2, 11, 12, 13, 2, 15, 2, 17, 2, 19, 4, 21, 2, 23, 4, 25, 2, 27, 4, 29, 30, 31, 2, 33, 2, 35, 12, 37, 2, 39, 20, 41, 6, 43, 4, 45, 2, 47, 12, 49, 2, 51, 4, 53, 2, 55, 56, 57, 2, 59, 4, 61, 2, 63, 2, 65, 6, 67, 4, 69, 14, 71, 4, 73, 2, 75, 4, 77, 2, 79, 20, 81, 2

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OFFSET

1,2

COMMENTS

For even n, a(n) is an even divisor of n.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

FORMULA

a(2k+1) = 2k+1. a(2k) = A058005(k).

MAPLE

swing := n -> n!/iquo(n, 2)!^2: seq(igcd(n, swing(n)), n=1..82); # Peter Luschny, May 17 2013

MATHEMATICA

a[n_] := GCD[n, Binomial[n, Floor[n/2]]]; Array[a, 100] (* Jean-François Alcover, Jun 03 2019 *)

PROG

(PARI) a(n) = gcd(n, binomial(n, n\2)); \\ Michel Marcus, Mar 22 2020

CROSSREFS

Cf. A001405, A049077.

Sequence in context: A007389 A007388 A348846 * A007387 A105222 A280503

Adjacent sequences: A057812 A057813 A057814 * A057816 A057817 A057818

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 13 2000

EXTENSIONS

Offset changed to 1 by Peter Luschny, May 17 2013

STATUS

approved