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
Keywords
Examples
a(7) = 1 + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 2 + 4 + 12 = 20.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *) -
PARI
a(n) = if (n==1, 1, 1+ sumdiv(n-1, d, a(d))); \\ Michel Marcus, Oct 30 2017
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
Comments