A372635 - OEIS

%I #15 May 08 2024 04:56:43

%S 1,4,16,36,100,144,324,484,784,1024,1764,2116,3364,4096,5184,6400,

%T 9216,10404,14400,16384,19600,22500,29584,32400,40000,44944,52900,

%U 58564,72900,77284,94864,104976,118336,129600,147456,156816,186624,202500,224676,240100,280900

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

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

%F a(n) = A002088(n)^2.

%F a(n) ~ 9*n^4/(Pi^4). - _Vaclav Kotesovec_, May 08 2024

%t nmax = 50; Accumulate[Table[EulerPhi[j], {j, 1, nmax}]]^2 (* _Vaclav Kotesovec_, May 08 2024 *)

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

%o (PARI) a(n) = sum(k=1, n, eulerphi(k))^2;

%Y Cf. A000010, A002088, A372633.

%K nonn

%O 1,2

%A _Seiichi Manyama_, May 08 2024