A067541 - OEIS

A067541

phi(n*(n+1)/2)/phi(n) where phi is the Euler totient function A000010(n).

1, 2, 1, 2, 2, 6, 2, 3, 4, 10, 2, 6, 6, 8, 4, 8, 6, 18, 4, 6, 10, 22, 4, 10, 12, 18, 6, 14, 8, 30, 8, 10, 16, 24, 6, 18, 18, 24, 8, 20, 12, 42, 10, 12, 22, 46, 8, 21, 20, 32, 12, 26, 18, 40, 12, 18, 28, 58, 8, 30, 30, 36, 16, 24, 20, 66, 16, 22, 24, 70, 12, 36, 36, 40, 18, 30, 24

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

Let n = 2^k*m, GCD(m, 2) = 1. Then a(n) = phi((n + 1)/2) if k = 0, phi(n + 1) if k = 1 and (phi(n + 1))/2 if k > 1. - Vladeta Jovovic, Feb 06 2002

a(n) = A000010(A000217(n))/A000010(n). - Michel Marcus, Nov 04 2013

EXAMPLE

a(6) = 6; phi(6*7/2)/phi(6) = phi(21)/phi(6) = 12/2 = 6.

MAPLE

with(numtheory); A067541:=n->phi(n*(n+1)/2)/phi(n); seq(A067541(k), k=1..100); # Wesley Ivan Hurt, Nov 04 2013

MATHEMATICA

Table[EulerPhi[n*(n+1)/2]/EulerPhi[n], {n, 1, 100}] (* Vincenzo Librandi, Mar 05 2013 *)

PROG

(PARI) a(n)=eulerphi(n*(n+1)/2)/eulerphi(n) \\ Charles R Greathouse IV, Mar 05 2013

(Magma) [EulerPhi(n*(n+1) div 2)/EulerPhi(n): n in [1..100]]; // Vincenzo Librandi, Mar 05 2013

CROSSREFS

Sequence in context: A093659 A306714 A200745 * A054706 A351082 A334500

Adjacent sequences: A067538 A067539 A067540 * A067542 A067543 A067544

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 28 2002

STATUS

approved