A190906 a(n) = gcd(n! / floor(n/2)!^2, 3^n).

1, 1, 1, 3, 3, 3, 1, 1, 1, 9, 9, 9, 3, 3, 3, 9, 9, 9, 1, 1, 1, 3, 3, 3, 1, 1, 1, 27, 27, 27, 9, 9, 9, 27, 27, 27, 3, 3, 3, 9, 9, 9, 3, 3, 3, 27, 27, 27, 9, 9, 9, 27, 27, 27, 1, 1, 1, 3, 3, 3, 1, 1, 1, 9, 9, 9, 3, 3, 3, 9, 9, 9, 1, 1, 1, 3, 3, 3, 1, 1, 1

Offset

0,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Formula

a(n) = gcd(A056040(n), 3^n).

a(n) <= n. - Charles R Greathouse IV, Jun 30 2011

From Johannes W. Meijer, Jun 30 2011: (Start)

a(3*n) = a(3*n+1) = a(3*n+2) = A010684(n)*a(n) for n > 1 with a(0) = a(1) = a(2) = 1.

a(9*n+3) = a(9*n+4) = a(9*n+5) = 3*a(n).

a(9*n) = a(9*n+1) = a(9*n+2) = a(9*n+6) = a(9*n+7) = a(9*n+8) = A010690(n)*a(n). (End)

Maple

A190906 := n -> igcd(n!/iquo(n, 2)!^2, 3^n): seq(A190906(n), n=0..80);

Mathematica

sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[n_] := GCD[sf[n], 3^n]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jul 29 2013 *)

Prog

(PARI) a(n)=gcd(n!/(n\2)!^2, 3^n) \\ Charles R Greathouse IV, Jun 30 2011
(PARI) a(n)=my(s); while(n\=3, s+=n%2); 3^s \\ Charles R Greathouse IV, Jun 30 2011

Crossrefs

Cf. A060632.

Sequence in context: A131289 A130974 A064353 * A355586 A080311 A135368

Adjacent sequences: A190903 A190904 A190905 * A190907 A190908 A190909

Keyword

nonn,easy,look,hear

Author

Peter Luschny, Jun 30 2011

Status

approved