|
%I #37 Sep 08 2022 08:45:56
%S 1,8,54,128,500,432,2058,2048,4374,4000,13310,6912,26364,16464,27000,
%T 32768,78608,34992,123462,64000,111132,106480,267674,110592,312500,
%U 210912,354294,263424,682892,216000,893730,524288,718740,628864,1029000,559872
%N a(n) = phi(n^4).
%H Vincenzo Librandi and T. D. Noe, <a href="/A189393/b189393.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..680 from Vincenzo Librandi)
%F a(n) = n^3*phi(n).
%F Dirichlet g.f.: zeta(s - 4) / zeta(s - 3). The n-th term of the Dirichlet inverse is n^3 * A023900(n) = (-1)^omega(n) * a(n) / A003557(n), where omega=A001221. - _Álvar Ibeas_, Nov 24 2017
%F Sum_{k=1..n} a(k) ~ 6*n^5 / (5*Pi^2). - _Vaclav Kotesovec_, Feb 02 2019
%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^5 - p^4 - p + 1)) = 1.15762316629211803144... - _Amiram Eldar_, Dec 06 2020
%t EulerPhi[Range[100]^4] (* _T. D. Noe_, Dec 27 2011 *)
%o (Magma) [ n^3*EulerPhi(n) : n in [1..100] ]
%o (PARI) vector(66,n,n^3*eulerphi(n)) /* _Joerg Arndt_, Apr 22 2011 */
%Y Cf. A002618 (phi(n^2)), A053191 (phi(n^3)), A238533 (phi(n^5)), A239442 (phi(n^7)), A239443 (phi(n^9)).
%K nonn,easy,mult
%O 1,2
%A _Vincenzo Librandi_, Apr 21 2011
|
