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A241665 Number of iterations of A241663 needed to reach either 0 or 1.

%I A241665 #24 Feb 03 2025 13:52:08
%S A241665 1,1,1,1,1,1,2,1,1,1,3,1,2,1,1,1,3,1,2,1,1,1,3,1,2,1,1,1,3,1,2,1,1,1,
%T A241665 2,1,2,1,1,1,3,1,2,1,1,1,3,1,2,1,1,1,3,1,3,1,1,1,4,1,2,1,1,1,2,1,2,1,
%U A241665 1,1,3,1,2,1,1,1,2,1,2,1,1,1,3,1,3,1,1,1,4,1,2,1,1,1,2,1,2,1,1,1,3,1,2,1,1
%N A241665 Number of iterations of A241663 needed to reach either 0 or 1.
%C A241665 It might be more natural to define the initial terms as a(0) = a(1) = 0 for the sake of recurrence. - _Antti Karttunen_, Oct 01 2018
%H A241665 Antti Karttunen, <a href="/A241665/b241665.txt">Table of n, a(n) for n = 1..65537</a>
%H A241665 C. Defant, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Defant/defant5.html">On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions</a>, J. Int. Seq. 18 (2015) # 15.2.1
%H A241665 Colin Defant, <a href="/A241665/a241665.py.txt">Python program</a>
%e A241665 A241663(11)=7, A241663(7)=3, A241663(3)=0. Thus, a(11)=3.
%o A241665 (Python) # See Defant link. Enter m=4, as well as starting and ending values of n. The third string of numbers will be this sequence.
%o A241665 (PARI)
%o A241665 A241663(n) = {my(f = factor(n)); prod(i=1, #f~, if ((f[i, 1] == 2) || (f[i, 1] == 3), 0, f[i, 1]^(f[i, 2]-1)*(f[i, 1]-4))); } \\ From A241663
%o A241665 A241665(n) = { my(s=(1==n)); while(n>1, n = A241663(n); s++); (s); }; \\ _Antti Karttunen_, Oct 01 2018
%Y A241665 Cf. A241663, A241668.
%K A241665 nonn
%O A241665 1,7
%A A241665 _Colin Defant_, Apr 26 2014
%E A241665 More terms from _Alois P. Heinz_, Apr 30 2014
%E A241665 Terms a(88) .. a(105) from _Antti Karttunen_, Oct 01 2018