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A349825 Number of steps when x -> A349824(x) is iterated starting at n needed to reach fixed point or 28, or -1 if trajectory increases for ever or ends in a nontrivial loop other than (28,33).

%I A349825 #9 Jan 02 2022 07:24:40
%S A349825 0,1,0,0,9,0,10,0,8,4,9,0,3,0,8,9,8,0,7,0,1,2,2,0,6,2,1,0,0,0,0,0,7,1,
%T A349825 8,7,5,0,7,8,4,0,6,0,3,2,7,0,9,1,6,5,6,0,4,8,7,4,12,0,10,0,11,9,12,6,
%U A349825 10,0,10,7,7,0,11,0,6,9,8,6,5,0,7,10,9,0
%N A349825 Number of steps when x -> A349824(x) is iterated starting at n needed to reach fixed point or 28, or -1 if trajectory increases for ever or ends in a nontrivial loop other than (28,33).
%C A349825 It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33).
%C A349825 a(n) = number of steps to reach A349826(n) (or -1).
%H A349825 Rémy Sigrist, <a href="/A349825/b349825.txt">Table of n, a(n) for n = 0..10000</a>
%e A349825 Trajectory of 16 is 16, 32, 50, 36, 40, 44, 45, 33, 28, 33, 28, 33, 28, 33, 28, 33, 28, 33, 28, ..., reaching low point of 28 after 8 steps, so a(16) = 8.
%o A349825 (PARI) a(n) = { for (k=0, oo, my (m=if (n==0, 0, my (f=factor(n)); bigomega(f)*sum(k=1, #f~, f[k,1]*f[k,2]))); if (n==28 || m==n, return (k), n=m) ) } \\ _Rémy Sigrist_, Jan 02 2022
%Y A349825 Cf. A349824-A349827.
%K A349825 nonn
%O A349825 0,5
%A A349825 _N. J. A. Sloane_, Jan 01 2022
%E A349825 More terms from _Rémy Sigrist_, Jan 02 2022