A306412 - OEIS

%I #18 Dec 06 2020 02:50:49

%S 1,128,4374,32768,312500,559872,4941258,8388608,28697814,40000000,

%T 194871710,143327232,752982204,632481024,1366875000,2147483648,

%U 6565418768,3673320192,16089691302,10240000000,21613062492,24943578880,74906159834,36691771392,122070312500

%N a(n) = phi(n^8) = n^7*phi(n).

%H Amiram Eldar, <a href="/A306412/b306412.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (p - 1)*p^(8*e-1).

%F Dirichlet g.f.: zeta(s - 8) / zeta(s - 7).

%F Sum_{k=1..n} a(k) ~ 2*n^9 / (3*Pi^2). See A239443 for a more general formula.

%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^9 - p^8 - p + 1)) = 1.00807702579309679541... - _Amiram Eldar_, Dec 06 2020

%t Table[n^7*EulerPhi[n], {n, 1, 25}] (* _Amiram Eldar_, Dec 06 2020 *)

%o (PARI) a(n) = n^7 * eulerphi(n)

%Y Eulerphi(n^e): A000010 (e=1), A002618 (e=2), A053191 (e=3), A189393 (e=4), A238533 (e=5), A306411 (e=6), A239442 (e=7), this sequence (e=8), A239443 (e=9).

%K nonn,easy,mult

%O 1,2

%A _Jianing Song_, Feb 13 2019