A375478 Irregular triangle read by rows in which row n lists the iterates of the phi(x) map from n to 1, where phi(x) is Euler's totient function (A000010).

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

Offset: 1

Author

Paolo Xausa, Aug 17 2024

Keywords

• nonn
• tabf
• easy

Comments

First differs from A246700 at n = 22.

Examples

			Triangle begins:
   1;
   2, 1;
   3, 2, 1;
   4, 2, 1;
   5, 4, 2, 1;
   6, 2, 1;
   7, 6, 2, 1;
   8, 4, 2, 1;
   9, 6, 2, 1;
  10, 4, 2, 1;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10636 (rows 1..1200 of the triangle, flattened).
• Index entries for sequences related to totient function phi(n).

Crossrefs

Supersequence of A246700.

Cf. A000010, A049108 (row lengths), A053478 (row sums).

Programs

Mathematica

Array[Most[FixedPointList[EulerPhi, #]] &, 25]

Formula

T(n,1) = n; T(n,k) = A000010(T(n,k-1)), for k = 2..A049108(n).