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a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(2*j*k) / phi(k).
1

%I #10 May 09 2024 07:00:54

%S 1,9,21,55,93,163,241,383,507,709,915,1205,1497,1907,2220,2794,3306,

%T 3966,4610,5438,6075,7113,8067,9245,10272,11742,12900,14552,16086,

%U 17798,19552,21894,23532,26082,27933,30589,33105,36307,38619,41945,45049,48459,51875

%N a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(2*j*k) / phi(k).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.

%t Table[Sum[Sum[EulerPhi[2*j*k], {j, 1, n}]/EulerPhi[k], {k, 1, n}], {n, 1, 50}] (* _Vaclav Kotesovec_, May 09 2024 *)

%o (PARI) a(n) = sum(j=1, n, sum(k=1, n, eulerphi(2*j*k)/eulerphi(k)));

%Y Cf. A000010, A372636, A372665.

%K nonn

%O 1,2

%A _Seiichi Manyama_, May 09 2024