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%I #40 Jun 19 2022 02:21:30
%S 1,5,19,37,101,95,295,293,505,505,1211,703,2029,1475,1919,2341,4625,
%T 2525,6499,3737,5605,6055,11639,5567,12601,10145,13627,10915,23549,
%U 9595,28831,18725,23009,23125,29795,18685,49285,32495,38551,29593
%N a(n) = Sum_{d|n} phi(d^3).
%H Harvey P. Dale, <a href="/A068963/b068963.txt">Table of n, a(n) for n = 1..1000</a>
%F Also Sum_{d|n} d*phi(d^2), or Sum_{d|n} d^2*phi(d).
%F Also Sum_{k=1..n} (n/gcd(n, k))^2 = Sum_{k=1..n} (lcm(n, k)/k)^2. - _Vladeta Jovovic_, Dec 29 2002
%F Multiplicative with a(p^e) = 1 + p^2 * (p-1)*(p^(3e)-1)/(p^3-1).
%F G.f.: Sum_{k>=1} k^2*phi(k)*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Mar 10 2018
%F Dirichlet g.f.: Sum_{n>=1} a(n) / n^s = zeta(s) * zeta(s-3) / zeta(s-2). - _Werner Schulte_, Feb 18 2021
%F Sum_{k=1..n} a(k) ~ Pi^2 * n^4 / 60. - _Vaclav Kotesovec_, Aug 20 2021
%t Table[Total[EulerPhi[Divisors[n]^3]],{n,50}] (* _Harvey P. Dale_, Feb 24 2013 *)
%t f[p_, e_] := p^2*(p - 1)*(p^(3 e) - 1)/(p^3 - 1) + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 40] (* _Amiram Eldar_, Jun 19 2022 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d^3)); \\ _Michel Marcus_, Mar 10 2018
%Y Cf. A000010, A057660, A056789.
%K easy,nonn,mult
%O 1,2
%A _Benoit Cloitre_, Apr 06 2002
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