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A068336
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a(1) = 1; a(n+1) = 1 + sum{k|n} a(k), sum is over the positive divisors, k, of n.
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12
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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
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OFFSET
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1,2
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COMMENTS
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Equals row sums of triangle A160182. - Gary W. Adamson, May 03 2009
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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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
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EXAMPLE
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a(7) = 1 + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 2 + 4 + 12 = 20.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A003238, A027750, A160182.
Sequence in context: A339736 A064374 A000885 * A293821 A194944 A133871
Adjacent sequences: A068333 A068334 A068335 * A068337 A068338 A068339
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet, Feb 27 2002
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STATUS
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approved
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