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A372636 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k) / phi(k).

%I A372636 #23 Feb 16 2025 08:34:06
%S A372636 1,5,14,31,58,93,148,219,306,407,550,695,898,1103,1323,1610,1963,2293,
%T A372636 2738,3152,3597,4116,4773,5362,6073,6808,7611,8437,9492,10348,11557,
%U A372636 12728,13868,15143,16425,17753,19482,21083,22687,24350,26481,28186,30535,32641
%N A372636 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k) / phi(k).
%H A372636 Vaclav Kotesovec, <a href="/A372636/b372636.txt">Table of n, a(n) for n = 1..10000</a>
%H A372636 Vaclav Kotesovec, <a href="/A372636/a372636.jpg">Plot of a(n)/n^3 for n = 1..10000</a>
%H A372636 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F A372636 a(n) ~ c * n^3, where c = A330596 / 2 = 0.374267629841... . - _Amiram Eldar_, May 09 2024
%t A372636 Table[Sum[Sum[EulerPhi[j*k], {j, 1, n}] / EulerPhi[k], {k, 1, n}], {n, 1, 50}] (* _Vaclav Kotesovec_, May 08 2024 *)
%t A372636 s = 1; Join[{1}, Table[s += Sum[EulerPhi[j*n] / EulerPhi[j], {j, 1, n}] + Sum[EulerPhi[j*n], {j, 1, n-1}] / EulerPhi[n], {n, 2, 50}]] (* _Vaclav Kotesovec_, May 08 2024 *)
%o A372636 (PARI) a(n) = sum(j=1, n, sum(k=1, n, eulerphi(j*k)/eulerphi(k)));
%Y A372636 Cf. A330596, A372619, A372633.
%K A372636 nonn
%O A372636 1,2
%A A372636 _Seiichi Manyama_, May 08 2024