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A372633 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k).

%I A372633 #28 Feb 16 2025 08:34:06
%S A372633 1,5,19,47,115,183,369,585,927,1271,2021,2557,3817,4813,6101,7749,
%T A372633 10581,12381,16395,19147,22855,26795,33901,38141,46081,52729,61711,
%U A372633 69487,83851,90731,108341,121749,136929,152065,171097,185257,215101,236377,261553,283153,323993
%N A372633 a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k).
%H A372633 Vaclav Kotesovec, <a href="/A372633/b372633.txt">Table of n, a(n) for n = 1..10000</a>
%H A372633 Vaclav Kotesovec, <a href="/A372633/a372633.jpg">Plot of a(n)/n^4 for n = 1..100000</a>
%H A372633 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F A372633 a(n) ~ c * n^4, where c = A065464 / 4 = 0.107062376419... . - _Amiram Eldar_, May 09 2024
%t A372633 Table[Sum[EulerPhi[i*j], {i, 1, n}, {j, 1, n}], {n, 1, 50}] (* _Vaclav Kotesovec_, May 08 2024 *)
%t A372633 s = 1; Join[{1}, Table[s += EulerPhi[n^2] + 2*Sum[EulerPhi[j*n], {j, 1, n-1}], {n, 2, 50}]] (* _Vaclav Kotesovec_, May 08 2024 *)
%o A372633 (PARI) a(n) = sum(j=1, n, sum(k=1, n, eulerphi(j*k)));
%Y A372633 Cf. A000010, A002088, A057434, A065464, A372606, A372635.
%K A372633 nonn,nice
%O A372633 1,2
%A A372633 _Seiichi Manyama_, May 08 2024