OFFSET
1,2
COMMENTS
The number of elements of the wreath product of C_n and S_6 with cycle partition equal to (6*n) is equal to 5!*a(n), where C_n is the cyclic group of order n, S_6 the symmetric group on 6 elements. - Josaphat Baolahy, Mar 13 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = (p - 1)*p^(6*e-1).
Dirichlet g.f.: zeta(s - 6) / zeta(s - 5).
Sum_{k=1..n} a(k) ~ 6*n^7 / (7*Pi^2). See A239443 for a more general formula.
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/(p^7 - p^6 - p + 1)) = 1.03396580456393429553879930771676667947490034699829164744357501993310897305... - Vaclav Kotesovec, Sep 20 2020
MATHEMATICA
Array[EulerPhi[#] #^5 &, 34] (* Michael De Vlieger, Feb 17 2019 *)
PROG
(PARI) a(n) = n^5 * eulerphi(n)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jianing Song, Feb 13 2019
STATUS
approved