|
| |
|
|
A344201
|
|
Number of cyclic subgroups of the group (C_n)^n, where C_n is the cyclic group of order n.
|
|
1
|
|
|
|
1, 4, 14, 136, 782, 23360, 137258, 4210816, 64576643, 2500000768, 28531167062, 2229573502976, 25239592216022, 1852001137606656, 54736740117685528, 2305878194659557376, 51702516367896047762, 6557734713069408616448, 109912203092239643840222
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} phi(x_1)*phi(x_2)* ... *phi(x_n)/phi(lcm(x_1, x_2, ... , x_n)).
a(n) = Sum_{d|n} b(d, n), where b(n, k) = ( Sum_{d|n} mu(n/d) * d^k )/phi(n).
If p is prime, a(p) = 1 + (p^p - 1)/(p - 1).
|
|
|
MATHEMATICA
|
b[n_, k_] := DivisorSum[n, MoebiusMu[n/#] * #^k &] / EulerPhi[n]; a[n_] := DivisorSum[n, b[#, n] &]; Array[a, 20] (* Amiram Eldar, Oct 04 2023 *)
|
|
|
PROG
|
(PARI) b(n, k) = sumdiv(n, d, moebius(n/d)*d^k)/eulerphi(n);
a(n) = sumdiv(n, d, b(d, n));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
