A068336 - OEIS

%I #26 Jun 09 2021 11:14:03

%S 1,2,4,6,10,12,20,22,32,38,52,54,80,82,106,122,154,156,208,210,268,

%T 294,350,352,454,466,550,588,700,702,876,878,1032,1090,1248,1280,1548,

%U 1550,1762,1848,2138,2140,2530,2532,2888,3042,3396,3398,3974,3996,4502

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

%C Equals row sums of triangle A160182. - _Gary W. Adamson_, May 03 2009

%H Reinhard Zumkeller, <a href="/A068336/b068336.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 a(7) = 1 + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 2 + 4 + 12 = 20.

%t 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 (Haskell)

%o a068336 n = a068336_list !! (n-1)

%o a068336_list = 1 : f 1 where

%o    f x = (1 + sum (map a068336 $ a027750_row x)) : f (x + 1)

%o -- _Reinhard Zumkeller_, Dec 20 2014

%o (PARI) a(n) = if (n==1, 1, 1+ sumdiv(n-1, d, a(d))); \\ _Michel Marcus_, Oct 30 2017

%Y Cf. A003238, A027750, A160182.

%K nonn

%O 1,2

%A _Leroy Quet_, Feb 27 2002