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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).
4

%I #19 Aug 18 2024 16:03:58

%S 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,

%T 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,

%U 4,2,1,18,6,2,1,19,18,6,2,1,20,8,4,2,1,21,12,4,2,1

%N 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).

%C First differs from A246700 at n = 22.

%H Paolo Xausa, <a href="/A375478/b375478.txt">Table of n, a(n) for n = 1..10636</a> (rows 1..1200 of the triangle, flattened).

%H <a href="/index/To#totient">Index entries for sequences related to totient function phi(n)</a>.

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

%e Triangle begins:

%e 1;

%e 2, 1;

%e 3, 2, 1;

%e 4, 2, 1;

%e 5, 4, 2, 1;

%e 6, 2, 1;

%e 7, 6, 2, 1;

%e 8, 4, 2, 1;

%e 9, 6, 2, 1;

%e 10, 4, 2, 1;

%e ...

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

%Y Supersequence of A246700.

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

%K nonn,tabf,easy

%O 1,2

%A _Paolo Xausa_, Aug 17 2024