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

Author

Hartmut F. W. Hoft, Feb 04 2024

Keywords

• nonn
• tabf

Examples

			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 }.
		

Crossrefs

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

Programs

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 *)