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A361151 a(n) = K(n-1) + K(n) + K(n+1), where K(n) = A341711(floor(n/2)).

%I A361151 #13 Dec 01 2023 15:58:00
%S A361151 2,7,11,29,43,97,137,283,389,749,1003,1839,2421,4259,5515,9391,12011,
%T A361151 19887,25143,40665,50931,80679,100161,155847,192051,294047,359839,
%U A361151 543127,660623,984239,1190359,1752799,2109119,3072351,3679263,5307023,6327871,9044395
%N A361151 a(n) = K(n-1) + K(n) + K(n+1), where K(n) = A341711(floor(n/2)).
%e A361151 n=4: 5+19+19 = 43 = a(4).
%p A361151 with(numtheory):
%p A361151 b:= proc(n) option remember; nops(invphi(n)) end:
%p A361151 g:= proc(n) option remember; `if`(n=0, 1, add(
%p A361151       g(n-j)*add(d*b(d), d=divisors(j)), j=1..n)/n)
%p A361151     end:
%p A361151 a:= n-> add(g(2*floor((i+n)/2)+1)/2, i=-1..1):
%p A361151 seq(a(n), n=0..40);  # _Alois P. Heinz_, Mar 02 2023
%t A361151 nmax1 = 40;
%t A361151 terms = nmax1 + 2; (* number of terms of A120963 *)
%t A361151 nmax2 = Floor[terms/2] - 1;
%t A361151 S[m_] := S[m] = CoefficientList[Product[1/(1 - x^EulerPhi[k]), {k, 1, m*terms}] + O[x]^(terms + 1), x];
%t A361151 S[m = 1]; S[m++]; While[S[m] != S[m - 1], m++];
%t A361151 A120963 = S[m];
%t A361151 A341711[n_ /; 0 <= n <= nmax2] := A120963[[2 n + 2]]/2;
%t A361151 K[n_] := A341711[Floor[n/2]];
%t A361151 a[n_] := If[n == 0, 2, K[n - 1] + K[n] + K[n + 1]];
%t A361151 Table[a[n], {n, 0, nmax1}] (* _Jean-François Alcover_, Dec 01 2023 *)
%Y A361151 Cf. A341711.
%K A361151 nonn
%O A361151 0,1
%A A361151 _N. J. A. Sloane_, Mar 02 2023