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a(1) = a(2) = 1; a(n+2) = 1 + Sum_{d|n} a(d).
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%I #7 Dec 06 2022 10:01:04

%S 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 174,46,191,58,241,60,289,62,353,78,380,90,490,92,519,110,640,112,723,

%U 114,851,146,892,148,1113,156,1177,184,1371,186,1500,204,1752,234,1813

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

%H Robert Israel, <a href="/A346117/b346117.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f. A(x) satisfies: A(x) = x + x^2 * (1 / (1 - x) + A(x) + A(x^2) + A(x^3) + ...).

%p f:= proc(n) option remember; local d; 1 + add(procname(d), d = numtheory:-divisors(n-2)) end proc:

%p f(1):= 1: f(2):= 1:

%p map(f, [$1..60]); # _Robert Israel_, Dec 02 2022

%t a[1] = a[2] = 1; a[n_] := a[n] = 1 + Sum[a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 60}]

%t 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 Cf. A007439, A068336.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Jul 05 2021