A062624 Number of integers less than A000108(n) relatively prime to A000108(n).

1, 1, 1, 4, 6, 12, 40, 240, 480, 1920, 6912, 20736, 76032, 253440, 608256, 4257792, 7983360, 26611200, 88704000, 319334400, 1277337600, 5109350400, 19508428800, 73156608000, 336520396800, 1177821388800, 6281714073600, 23332080844800, 66663088128000

Offset: 0

Author

Jason Earls, Jul 04 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Florian Luca and Pantelimon Stanica, On the Euler function of the Catalan numbers, Journal of Number Theory, Vol. 132, No. 7 (2012), pp. 1404-1424.

Crossrefs

Cf. A000010, A000108.

Programs

Maple

with(numtheory): a:= n-> phi(binomial(2*n,n)/(n+1)): seq(a(n), n=0..27); # Zerinvary Lajos, Oct 05 2007

Mathematica

a[n_] := EulerPhi[CatalanNumber[n]]; Array[a, 30, 0] (* Amiram Eldar, Nov 27 2024 *)

PARI

a(n) = eulerphi(binomial(2*n, n)/(n + 1));

Sage

[euler_phi(binomial(2*n,n)/(n+1))for n in range(0,28)] # Zerinvary Lajos, Jun 06 2009

Formula

a(n) = phi(binomial(2n, n)/(n+1)).

a(n) = A000010(A000108(n)).