A246700 Table read by rows: trajectories under iteration of Carmichael's lambda function (cf. A002322).

1, 2, 1, 3, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 2, 1, 7, 6, 2, 1, 8, 2, 1, 9, 6, 2, 1, 10, 4, 2, 1, 11, 10, 4, 2, 1, 12, 2, 1, 13, 12, 2, 1, 14, 6, 2, 1, 15, 4, 2, 1, 16, 4, 2, 1, 17, 16, 4, 2, 1, 18, 6, 2, 1, 19, 18, 6, 2, 1, 20, 4, 2, 1, 21, 6, 2, 1, 22, 10, 4, 2, 1

Offset: 1

Author

Reinhard Zumkeller, Sep 02 2014

Keywords

• nonn
• tabf

Comments

Length of row n = A185816(n) + 1.

Examples

			.   |  1 | 1             | 13 | 13-12-2-1        | 25 | 25-20-4-2-1
.   |  2 | 2-1           | 14 | 14-6-2-1         | 26 | 26-12-2-1
.   |  3 | 3-2-1         | 15 | 15-4-2-1         | 27 | 27-18-6-2-1
.   |  4 | 4-2-1         | 16 | 16-4-2-1         | 28 | 28-6-2-1
.   |  5 | 5-4-2-1       | 17 | 17-16-4-2-1      | 29 | 29-28-6-2-1
.   |  6 | 6-2-1         | 18 | 18-6-2-1         | 30 | 30-4-2-1
.   |  7 | 7-6-2-1       | 19 | 19-18-6-2-1      | 31 | 31-30-4-2-1
.   |  8 | 8-2-1         | 20 | 20-4-2-1         | 32 | 32-8-2-1
.   |  9 | 9-6-2-1       | 21 | 21-6-2-1         | 33 | 33-10-4-2-1
.   | 10 | 10-4-2-1      | 22 | 22-10-4-2-1      | 34 | 34-16-4-2-1
.   | 11 | 11-10-4-2-1   | 23 | 23-22-10-4-2-1   | 35 | 35-12-2-1
.   | 12 | 12-2-1        | 24 | 24-2-1           | 36 | 36-6-2-1  .
		

Links

• Reinhard Zumkeller, Rows n = 1..1001 of triangle, flattened

Crossrefs

Cf. A002322, A185816, A375478.

Programs

Haskell

import Data.List (genericIndex)
a246700 n k = genericIndex a246700_tabf (n - 1) !! (k-1)
a246700_row n = genericIndex a246700_tabf (n - 1)
a246700_tabf = [1] : f 2  where
   f x = (x : a246700_row (a002322 x)) : f (x + 1)

Mathematica

Array[Most[FixedPointList[CarmichaelLambda, #]] &, 25] (* Paolo Xausa, Aug 17 2024 *)

Formula

T(n,1) = n and T(n,k+1) = A002322(T(n,k)), k = 1..A185816(n).