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A360520 a(n) = A120963(n) + A341711(floor(n/2)).

%I A360520 #17 Nov 16 2023 19:06:28
%S A360520 2,3,11,15,43,57,137,177,389,495,1003,1257,2421,3003,5515,6771,12011,
%T A360520 14631,25143,30399,50931,61197,100161,119643,192051,228255,359839,
%U A360520 425631,660623,778119,1190359,1396479,2109119,2465439,3679263,4286175,6327871,7348719
%N A360520 a(n) = A120963(n) + A341711(floor(n/2)).
%H A360520 Jean-François Alcover, <a href="/A360520/b360520.txt">Table of n, a(n) for n = 0..1000</a>
%e A360520 n=4: a(4) = A120963(4) + A341711(2) = 24 + 19 = 43.
%p A360520 with(numtheory):
%p A360520 b:= proc(n) option remember; nops(invphi(n)) end:
%p A360520 g:= proc(n) option remember; `if`(n=0, 1, add(
%p A360520       g(n-j)*add(d*b(d), d=divisors(j)), j=1..n)/n)
%p A360520     end:
%p A360520 a:= n-> g(n)+g(2*iquo(n, 2)+1)/2:
%p A360520 seq(a(n), n=0..40);  # _Alois P. Heinz_, Mar 02 2023
%t A360520 b[n_] := b[n] = Length[invphi[n]];
%t A360520 g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j]*Sum[d*b[d], {d, Divisors[j]}], {j, 1, n}]/n];
%t A360520 a[n_] := g[n] + g[2*Quotient[n, 2] + 1]/2;
%t A360520 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 16 2023, after _Alois P. Heinz_ and using Maxim Rytin's invphi program (see A007617) *)
%Y A360520 Cf. A120963, A341711.
%K A360520 nonn
%O A360520 0,1
%A A360520 _N. J. A. Sloane_, Mar 02 2023