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A068336 a(1) = 1; a(n+1) = 1 + sum{k|n} a(k), sum is over the positive divisors, k, of n.

%I A068336 #26 Jun 09 2021 11:14:03
%S A068336 1,2,4,6,10,12,20,22,32,38,52,54,80,82,106,122,154,156,208,210,268,
%T A068336 294,350,352,454,466,550,588,700,702,876,878,1032,1090,1248,1280,1548,
%U A068336 1550,1762,1848,2138,2140,2530,2532,2888,3042,3396,3398,3974,3996,4502
%N A068336 a(1) = 1; a(n+1) = 1 + sum{k|n} a(k), sum is over the positive divisors, k, of n.
%C A068336 Equals row sums of triangle A160182. - _Gary W. Adamson_, May 03 2009
%H A068336 Reinhard Zumkeller, <a href="/A068336/b068336.txt">Table of n, a(n) for n = 1..10000</a>
%F A068336 G.f. A(x) satisfies: A(x) = x * (1 + x / (1 - x) + A(x) + A(x^2) + A(x^3) + ...). - _Ilya Gutkovskiy_, Jun 09 2021
%e A068336 a(7) = 1 + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 2 + 4 + 12 = 20.
%t A068336 a[1] = 1; a[n_] := a[n] = 1 + Sum[a[k], {k, Divisors[n-1]}]; Table[ a[n], {n, 1, 51}] (* _Jean-François Alcover_, Dec 20 2011 *)
%o A068336 (Haskell)
%o A068336 a068336 n = a068336_list !! (n-1)
%o A068336 a068336_list = 1 : f 1 where
%o A068336    f x = (1 + sum (map a068336 $ a027750_row x)) : f (x + 1)
%o A068336 -- _Reinhard Zumkeller_, Dec 20 2014
%o A068336 (PARI) a(n) = if (n==1, 1, 1+ sumdiv(n-1, d, a(d))); \\ _Michel Marcus_, Oct 30 2017
%Y A068336 Cf. A003238, A027750, A160182.
%K A068336 nonn
%O A068336 1,2
%A A068336 _Leroy Quet_, Feb 27 2002