A369895 Irregular triangle of iteration steps of A063919 until the end of the terminal cycle is reached, read by rows.

1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 7, 1, 8, 1, 9, 1, 10, 8, 1, 11, 1, 12, 8, 1, 13, 1, 14, 10, 8, 1, 15, 9, 1, 16, 1, 17, 1, 18, 12, 8, 1, 19, 1, 20, 10, 8, 1, 21, 11, 1, 22, 14, 10, 8, 1, 23, 1, 24, 12, 8, 1, 25, 1, 26, 16, 1, 27, 1, 28, 12, 8, 1, 29, 1, 30, 42, 54

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Example

The beginning of the irregular triangle showing 3 terminal cycles ( 1 ), ( 6 ) and ( 30 42 54 ):
  1
  2    1
  3    1
  4    1
  5    1
  6
  7    1
  ...
  14  10   8   1
  ...
  30  42  54
  31  1
  ...
Row 1230 contains a non-monotone iteration that ends in the 5-cycle starting at A097035(3):
1230, 1794, 2238, 2250, 1530, 1710, {1890, 2142, 2178, 1482, 1878 }.

Mathematica

a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *)
a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#] == 1 &]] - n /; n > 1
iter[k_] := Most[NestWhileList[a063919, k, UnsameQ, All]]
a369895[n_] := Map[iter, Range[n]]
a369895[30] (* irregular triangle *)
Flatten[a369895[30]] (* sequence data *)

Crossrefs

Cf. A002827, A063919, A097024, A097030, A097031, A097034, A097035, A318882, A318883.

Sequence in context: A338759 A229994 A165818 * A194746 A198336 A365431

Adjacent sequences: A369892 A369893 A369894 * A369896 A369897 A369898

Keyword

nonn,tabf

Author

Hartmut F. W. Hoft, Feb 04 2024

Status

approved