|
%I #26 Sep 08 2022 08:45:05
%S 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,
%T 8,10,16,24,6,18,18,24,8,20,12,42,10,12,22,46,8,21,20,32,12,26,18,40,
%U 12,18,28,58,8,30,30,36,16,24,20,66,16,22,24,70,12,36,36,40,18,30,24
%N phi(n*(n+1)/2)/phi(n) where phi is the Euler totient function A000010(n).
%H Vincenzo Librandi, <a href="/A067541/b067541.txt">Table of n, a(n) for n = 1..1000</a>
%F 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
%F a(n) = A000010(A000217(n))/A000010(n). - _Michel Marcus_, Nov 04 2013
%e a(6) = 6; phi(6*7/2)/phi(6) = phi(21)/phi(6) = 12/2 = 6.
%p with(numtheory); A067541:=n->phi(n*(n+1)/2)/phi(n); seq(A067541(k), k=1..100); # _Wesley Ivan Hurt_, Nov 04 2013
%t Table[EulerPhi[n*(n+1)/2]/EulerPhi[n], {n, 1, 100}] (* _Vincenzo Librandi_, Mar 05 2013 *)
%o (PARI) a(n)=eulerphi(n*(n+1)/2)/eulerphi(n) \\ _Charles R Greathouse IV_, Mar 05 2013
%o (Magma) [EulerPhi(n*(n+1) div 2)/EulerPhi(n): n in [1..100]]; // _Vincenzo Librandi_, Mar 05 2013
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 28 2002
|
