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

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A003238, A027750, A160182.

Sequence in context: A064374 A000885 A372638 * A293821 A194944 A133871

Adjacent sequences: A068333 A068334 A068335 * A068337 A068338 A068339

Keyword

nonn

Author

Leroy Quet, Feb 27 2002

Status

approved