|
%I #19 Dec 17 2022 03:14:14
%S 1,1,2,2,4,2,7,4,6,4,10,4,12,7,8,8,16,6,18,8,14,10,22,8,20,12,18,14,
%T 28,8,30,16,20,16,28,12,36,18,24,16,40,14,42,20,24,22,46,16,49,20,32,
%U 24,52,18,40,28,36,28,58,16,60,30,42,32,48,20,66,32,44,28,70,24,72,36,40,36,70,24,78
%N a(n) = phi(7 * n)/6.
%H Michael De Vlieger, <a href="/A359102/b359102.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusTransform.html">Moebius Transform</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F G.f.: -Sum_{k>=1} mu(7 * k) * x^k / (1 - x^k)^2, where mu() is the Moebius function (A008683).
%F From _Amiram Eldar_, Dec 17 2022: (Start)
%F Multiplicative with a(7^e) = 7^e, and a(p^e) = (p-1)*p^(e-1) if p != 7.
%F Dirichlet g.f.: zeta(s-1)/(zeta(s)*(1-1/7^s)).
%F Sum_{k=1..n} a(k) ~ (49/(16*Pi^2)) * n^2. (End)
%t Array[EulerPhi[7 #]/6 &, 79] (* _Michael De Vlieger_, Dec 16 2022 *)
%o (PARI) a(n) = eulerphi(7*n)/6;
%o (PARI) my(N=80, x='x+O('x^N)); Vec(-sum(k=1, N, moebius(7*k)*x^k/(1-x^k)^2))
%Y Cf. A195459, A359101.
%Y Cf. A008653, A359099.
%K nonn,easy,mult
%O 1,3
%A _Seiichi Manyama_, Dec 16 2022
|
