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URL: https://oeis.org/A068336

⇱ A068336 - OEIS

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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.
12
1, 2, 4, 6, 10, 12, 20, 22, 32, 38, 52, 54, 80, 82, 106, 122, 154, 156, 208, 210, 268, 294, 350, 352, 454, 466, 550, 588, 700, 702, 876, 878, 1032, 1090, 1248, 1280, 1548, 1550, 1762, 1848, 2138, 2140, 2530, 2532, 2888, 3042, 3396, 3398, 3974, 3996, 4502
OFFSET
1,2
COMMENTS
Equals row sums of triangle A160182. - Gary W. Adamson, May 03 2009
LINKS
FORMULA
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
EXAMPLE
a(7) = 1 + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 2 + 4 + 12 = 20.
MATHEMATICA
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 *)
PROG
(Haskell)
a068336 n = a068336_list !! (n-1)
a068336_list = 1 : f 1 where
f x = (1 + sum (map a068336 $ a027750_row x)) : f (x + 1)
-- Reinhard Zumkeller, Dec 20 2014
(PARI) a(n) = if (n==1, 1, 1+ sumdiv(n-1, d, a(d))); \\ Michel Marcus, Oct 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 27 2002
STATUS
approved