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!)
A344304 Number of cyclic subgroups of the group (C_n)^8, where C_n is the cyclic group of order n. 4
1, 256, 3281, 32896, 97657, 839936, 960801, 4210816, 7176641, 25000192, 21435889, 107931776, 67977561, 245965056, 320412617, 538984576, 435984841, 1837220096, 943531281, 3212524672, 3152388081, 5487587584, 3559590241, 13815687296, 7629472657, 17402255616 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

László Tóth, On the number of cyclic subgroups of a finite abelian group, arXiv: 1203.6201 [math.GR], 2012.

FORMULA

a(n) = Sum_{x_1|n, x_2|n, ... , x_8|n} phi(x_1)*phi(x_2)* ... *phi(x_8)/phi(lcm(x_1, x_2, ... , x_8)).

Inverse Moebius transform of A160908.

If p is prime, a(p) = 1 + (p^8 - 1)/(p - 1).

PROG

(PARI) a160908(n) = sumdiv(n, d, moebius(n/d)*d^8)/eulerphi(n);

a(n) = sumdiv(n, d, a160908(d));

CROSSREFS

Cf. A060648, A064969, A280184, A344219, A344302, A344303, A344305, A344306.

Sequence in context: A236130 A236254 A236251 * A070056 A185575 A185933

Adjacent sequences:  A344301 A344302 A344303 * A344305 A344306 A344307

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, May 14 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 January 21 17:44 EST 2022. Contains 350479 sequences. (Running on oeis4.)