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A344305 Number of cyclic subgroups of the group (C_n)^9, where C_n is the cyclic group of order n. 4
1, 512, 9842, 131328, 488282, 5039104, 6725602, 33620224, 64576643, 250000384, 235794770, 1292530176, 883708282, 3443508224, 4805671444, 8606777600, 7411742282, 33063241216, 17927094322, 64125098496, 66193374884, 120726922240, 81870575522, 330890244608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

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_9|n} phi(x_1)*phi(x_2)* ... *phi(x_9)/phi(lcm(x_1, x_2, ... , x_9)).

Inverse Moebius transform of A160953.

If p is prime, a(p) = 1 + (p^9 - 1)/(p - 1).

PROG

(PARI) a160953(n) = sumdiv(n, d, moebius(n/d)*d^9)/eulerphi(n);

a(n) = sumdiv(n, d, a160953(d));

CROSSREFS

Cf. A060648, A064969, A280184, A344219, A344302, A344303, A344304, A344306.

Sequence in context: A255028 A247932 A090007 * A254797 A254837 A254560

Adjacent sequences:  A344302 A344303 A344304 * A344306 A344307 A344308

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, May 14 2021

STATUS

approved

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Last modified September 17 19:58 EDT 2021. Contains 347489 sequences. (Running on oeis4.)