A104191 Sum of Euler totient function between successive powers of two.

1, 3, 14, 54, 236, 920, 3730, 14862, 59776, 238856, 956110, 3823410, 15299542, 61193632, 244779854, 979111158, 3916558030, 15666093384, 62664665094, 250658276292, 1002634426882, 4010536846838, 16042149531756, 64168594080686, 256674403929154, 1026697590590342, 4106790388347028

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..44 (terms 0..36 from Charles R Greathouse IV)

Formula

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

a(n) ~ 4^n * 9/Pi^2. - Charles R Greathouse IV, Sep 05 2017

a(n) = A002088(2^(n+1)-1) - A002088(2^n-1). - R. J. Mathar, Jan 11 2019

a(n) = (A018805(2^(n+1)-1) - A018805(2^n-1)) / 2. - Colin Linzer, Aug 04 2025

Mathematica

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

Prog

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

Crossrefs

Cf. A002088.

Sequence in context: A179610 A343543 A166680 * A318125 A151540 A226466

Adjacent sequences: A104188 A104189 A104190 * A104192 A104193 A104194

Keyword

nonn

Author

Roger L. Bagula, Mar 12 2005

Extensions

a(20)-a(26) from Charles R Greathouse IV, Sep 05 2017

Status

approved