login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343490 a(n) = Sum_{k=1..n} 4^(gcd(k, n) - 1). 1
1, 5, 18, 70, 260, 1050, 4102, 16460, 65574, 262420, 1048586, 4195500, 16777228, 67112990, 268436040, 1073758360, 4294967312, 17179936830, 68719476754, 274878169880, 1099511636076, 4398047559730, 17592186044438, 70368748407000, 281474976711700, 1125899923619900 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

FORMULA

a(n) = Sum_{d|n} phi(n/d)*4^(d - 1) = A054611(n)/4.

G.f.: Sum_{k>=1} phi(k) * x^k / (1 - 4*x^k).

MATHEMATICA

a[n_] := Sum[4^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 26] (* Amiram Eldar, Apr 17 2021 *)

PROG

(PARI) a(n) = sum(k=1, n, 4^(gcd(k, n)-1));

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*4^(d-1));

(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-4*x^k)))

CROSSREFS

Column 4 of A343489.

Cf. A000010, A054611.

Sequence in context: A164051 A134764 A188177 * A302077 A322773 A145780

Adjacent sequences:  A343487 A343488 A343489 * A343491 A343492 A343493

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 17 2021

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 June 23 04:15 EDT 2021. Contains 345395 sequences. (Running on oeis4.)