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!)
A342541 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n)). 4
1, 2, 4, 5, 8, 10, 12, 14, 28, 28, 20, 62, 24, 54, 272, 68, 32, 198, 36, 676, 1224, 130, 44, 1348, 4136, 180, 3540, 3426, 56, 12632, 60, 1640, 22520, 304, 129456, 22370, 72, 378, 101808, 270952, 80, 192996, 84, 40630, 1867184, 550, 92, 551528, 1679700, 4198860, 2105408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = Sum_{d|n} phi(n/d) * phi(d)^(n/d).

If p is prime, a(p) = 2 *(p-1).

MATHEMATICA

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#) &]; Array[a, 50] (* Amiram Eldar, Mar 15 2021 *)

PROG

(PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(n/gcd(k, n)));

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

CROSSREFS

Cf. A000010, A029935, A342485, A342539, A342542, A342543.

Sequence in context: A323976 A188975 A115392 * A179509 A157007 A173509

Adjacent sequences:  A342538 A342539 A342540 * A342542 A342543 A342544

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 15 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 September 28 19:12 EDT 2021. Contains 347717 sequences. (Running on oeis4.)