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%I #33 Mar 25 2024 15:17:58
%S 1,32,486,2048,12500,15552,100842,131072,354294,400000,1610510,995328,
%T 4455516,3226944,6075000,8388608,22717712,11337408,44569782,25600000,
%U 49009212,51536320,141599546,63700992,195312500,142576512,258280326,206524416,574312172,194400000,858874530,536870912,782707860,726966784
%N a(n) = phi(n^6) = n^5*phi(n).
%C 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
%H Amiram Eldar, <a href="/A306411/b306411.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (p - 1)*p^(6*e-1).
%F Dirichlet g.f.: zeta(s - 6) / zeta(s - 5).
%F Sum_{k=1..n} a(k) ~ 6*n^7 / (7*Pi^2). See A239443 for a more general formula.
%F Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/(p^7 - p^6 - p + 1)) = 1.03396580456393429553879930771676667947490034699829164744357501993310897305... - _Vaclav Kotesovec_, Sep 20 2020
%t Array[EulerPhi[#] #^5 &, 34] (* _Michael De Vlieger_, Feb 17 2019 *)
%o (PARI) a(n) = n^5 * eulerphi(n)
%Y Eulerphi(n^e): A000010 (e=1), A002618 (e=2), A053191 (e=3), A189393 (e=4), A238533 (e=5), this sequence (e=6), A239442 (e=7), A306412 (e=8), A239443 (e=9).
%K nonn,easy,mult
%O 1,2
%A _Jianing Song_, Feb 13 2019
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