A104191 - OEIS

%I #18 Mar 26 2021 08:42:01

%S 1,3,14,54,236,920,3730,14862,59776,238856,956110,3823410,15299542,

%T 61193632,244779854,979111158,3916558030,15666093384,62664665094,

%U 250658276292,1002634426882,4010536846838,16042149531756,64168594080686,256674403929154,1026697590590342,4106790388347028

%N Sum of Euler totient function between successive powers of two.

%H Chai Wah Wu, <a href="/A104191/b104191.txt">Table of n, a(n) for n = 0..44</a> (terms 0..36 from Charles R Greathouse IV)

%F a(n) = phi(2^n) + phi(2^n + 1) + ... + phi(2^(n+1) - 2) + phi(2^(n+1) - 1).

%F a(n) ~ 4^n * 9/Pi^2. - _Charles R Greathouse IV_, Sep 05 2017

%F a(n) = A002088(2^(n+1)-1)-A002088(2^n-1). - _R. J. Mathar_, Jan 11 2019

%t Table[Sum[EulerPhi[i], {i, 2^n, 2^(n + 1) - 1}], {n, 0, 24}]

%o (PARI) a(n)=my(s); forfactored(k=2^n,2^(n+1)-1, s+=eulerphi(k)); s \\ _Charles R Greathouse IV_, Sep 05 2017

%Y Cf. A002088.

%K nonn

%O 0,2

%A _Roger L. Bagula_, Mar 12 2005

%E a(20)-a(26) from _Charles R Greathouse IV_, Sep 05 2017