login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034754 Dirichlet convolution of 3^(n-1) with phi(n). 6
1, 4, 11, 32, 85, 260, 735, 2224, 6585, 19780, 59059, 177472, 531453, 1595076, 4783175, 14351168, 43046737, 129147252, 387420507, 1162281440, 3486785925, 10460412292, 31381059631, 94143360944, 282429536825, 847289140932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..2096

FORMULA

a(n) ~ 3^(n-1). - Vaclav Kotesovec, Sep 11 2019

G.f.: Sum_{k>=1} phi(k) * x^k / (1 - 3*x^k). - Ilya Gutkovskiy, Feb 14 2020

a(n) = Sum_{k=1..n} 3^(gcd(k, n) - 1) = A054610(n)/3. - Seiichi Manyama, Apr 17 2021

a(n) = Sum_{k=1..n} 3^(n/gcd(n,k) - 1)*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 06 2021

MATHEMATICA

Table[Sum[3^(n/d - 1)*EulerPhi[d], {d, Divisors[n]}], {n, 1, 30}] (* Vaclav Kotesovec, Sep 10 2019 *)

PROG

(PARI) a(n) = sum(k=1, n, 3^(gcd(k, n)-1)); \\ Seiichi Manyama, Apr 17 2021

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*3^(d-1)); \\ Seiichi Manyama, Apr 17 2021

(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-3*x^k))) \\ Seiichi Manyama, Apr 17 2021

CROSSREFS

Cf. A000010, A001867, A034738, A054610.

Sequence in context: A155962 A027153 A319918 * A345029 A268744 A038747

Adjacent sequences:  A034751 A034752 A034753 * A034755 A034756 A034757

KEYWORD

nonn

AUTHOR

Erich Friedman

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)