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A346117 a(1) = a(2) = 1; a(n+2) = 1 + Sum_{d|n} a(d).

%I A346117 #7 Dec 06 2022 10:01:04
%S A346117 1,1,2,3,4,6,6,11,8,17,12,24,14,38,16,47,24,64,26,83,28,110,38,125,40,
%T A346117 174,46,191,58,241,60,289,62,353,78,380,90,490,92,519,110,640,112,723,
%U A346117 114,851,146,892,148,1113,156,1177,184,1371,186,1500,204,1752,234,1813
%N A346117 a(1) = a(2) = 1; a(n+2) = 1 + Sum_{d|n} a(d).
%H A346117 Robert Israel, <a href="/A346117/b346117.txt">Table of n, a(n) for n = 1..10000</a>
%F A346117 G.f. A(x) satisfies: A(x) = x + x^2 * (1 / (1 - x) + A(x) + A(x^2) + A(x^3) + ...).
%p A346117 f:= proc(n) option remember; local d; 1 + add(procname(d), d = numtheory:-divisors(n-2)) end proc:
%p A346117 f(1):= 1: f(2):= 1:
%p A346117 map(f, [$1..60]); # _Robert Israel_, Dec 02 2022
%t A346117 a[1] = a[2] = 1; a[n_] := a[n] = 1 + Sum[a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 60}]
%t A346117 nmax = 60; A[_] = 0; Do[A[x_] = x + x^2 (1/(1 - x) + Sum[A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y A346117 Cf. A007439, A068336.
%K A346117 nonn
%O A346117 1,3
%A A346117 _Ilya Gutkovskiy_, Jul 05 2021