%I #15 Nov 01 2022 04:52:22

%S 1,85,820,5440,16276,69700,120100,348160,597780,1383460,1786324,

%T 4460800,4855540,10208500,13346320,22282240,24221380,50811300,

%U 47176564,88541440,98482000,151837540,148316260,285491200,254312500,412720900,435781620,653344000,595531444

%N Jordan function ratio J_8(n)/J_2(n).

%F a(n) = A069093(n)/A007434(n) = A065960(n) * A065958(n).

%F Multiplicative with a(p^e) = p^(6*(e-1))*(p^2+1)*(p^4+1), e>0.

%F Dirichlet g.f.: zeta(s-6)*Product_{primes p} (1+p^(4-s)+p^(2-s)+p^(-s)).

%F Dirichlet convolution of A001014 with the multiplicative sequence 1, 21, 91, 0, 651, 1911, 2451, 0, 0, 13671, 14763, 0, 28731, 51471...

%F Sum_{k=1..n} a(k) ~ c * n^7 / 7, where c = Product_{primes p} (1 + 1/p^3 + 1/p^5 + 1/p^7) = 1.22847463998021088097249049512949441921891884186337179613337753... - _Vaclav Kotesovec_, Dec 18 2019

%t f[p_, e_] := p^(6*(e - 1))*(p^2 + 1)*(p^4 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 01 2022 *)

%Y Cf. A001014, A007434, A065958, A065960, A069093.

%K nonn,mult,easy

%O 1,2

%A _R. J. Mathar_, Aug 28 2011