cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A160183 Triangle, read by rows, obtained by dropping right diagonal from A160182.

Original entry on oeis.org

1, 2, 1, 3, 1, 1, 5, 2, 1, 1, 6, 2, 1, 1, 1, 10, 4, 2, 1, 1, 1, 11, 4, 2, 1, 1, 1, 1, 16, 6, 3, 2, 1, 1, 1, 1, 19, 7, 4, 2, 1, 1, 1, 1, 1, 26, 10, 5, 3, 2, 1, 1, 1, 1, 1
Offset: 1

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Author

Gary W. Adamson, May 03 2009

Keywords

Comments

A054525 * A160183 = triangle A160182. Mobius transform A054525 of the triangle shifts to the left adding I, I = Identity matrix.
Left border = A003238 starting (1, 2, 3, 5, 6, 10, 11, 16, 19,...).

Examples

			First few rows of the triangle =
1;
2, 1;
3, 1, 1;
5, 2, 1, 1;
6, 2, 1, 1, 1;
10, 4, 2, 1, 1, 1;
11, 4, 2, 1, 1, 1, 1;
16, 6, 3, 2, 1, 1, 1, 1;
19, 7, 4, 2, 1, 1, 1, 1, 1;
26, 10, 5, 3, 2, 1, 1, 1, 1, 1;
...
		

Crossrefs

Formula

A054525 * triangle A160182, also obtained by shifting triangle A160182 to the right, deleting the (1,1,1,...) right border.

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

Original entry on oeis.org

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

Views

Author

Leroy Quet, Feb 27 2002

Keywords

Comments

Equals row sums of triangle A160182. - Gary W. Adamson, May 03 2009

Examples

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

Crossrefs

Programs

  • 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
    
  • 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
Showing 1-2 of 2 results.