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A349827 Iterate x -> A349824(x) starting at n; a(n) is the greatest term in the trajectory, or -1 if the trajectory increases for ever.

%I A349827 #11 Jan 02 2022 07:24:52
%S A349827 0,1,2,3,45,5,45,7,45,27,45,11,27,13,45,50,50,17,45,19,27,27,30,23,45,
%T A349827 27,30,27,33,29,30,31,50,33,45,45,45,37,45,50,45,41,45,43,45,45,50,47,
%U A349827 55,49,50,51,52,53,54,55,56,57,66,59,60,61,66,63,72,65,66
%N A349827 Iterate x -> A349824(x) starting at n; a(n) is the greatest term in the trajectory, or -1 if the trajectory increases for ever.
%C A349827 It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33).
%H A349827 Rémy Sigrist, <a href="/A349827/b349827.txt">Table of n, a(n) for n = 0..10000</a>
%e A349827 Trajectory of 16 is 16, 32, 50, 36, 40, 44, 45, 33, 28, 33, 28, 33, 28, 33, 28, 33, 28, 33, 28, ..., ending at the loop (28, 33), and the high-point is 50, so a(16) = 50.
%o A349827 (PARI) a(n) = { my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=if (n==0, 0, my (f=factor(n)); bigomega(f)*sum(k=1, #f~, f[k,1]*f[k,2]))
%o A349827 ); s[#s] } \\ _Rémy Sigrist_, Jan 01 2022
%Y A349827 Cf. A349824-A349826.
%K A349827 nonn
%O A349827 0,3
%A A349827 _N. J. A. Sloane_, Jan 01 2022
%E A349827 More terms from _Rémy Sigrist_, Jan 01 2022