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A349826 Iterate x -> A349824(x) starting at n; if trajectory reaches a fixed point then that is a(n), if it ends in the loop (28,33) then a(n) = 28, otherwise a(n) = -1.

%I A349826 #10 Jan 02 2022 07:25:00
%S A349826 0,0,2,3,28,5,28,7,28,27,28,11,27,13,28,28,28,17,28,19,27,27,30,23,28,
%T A349826 27,30,27,28,29,30,31,28,28,28,28,28,37,28,28,28,41,28,43,28,28,28,47,
%U A349826 28,28,28,28,28,53,28,28,28,28,28,59,28,61,28,28,28,28,28
%N A349826 Iterate x -> A349824(x) starting at n; if trajectory reaches a fixed point then that is a(n), if it ends in the loop (28,33) then a(n) = 28, otherwise a(n) = -1.
%C A349826 It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33).
%H A349826 Rémy Sigrist, <a href="/A349826/b349826.txt">Table of n, a(n) for n = 0..10000</a>
%e A349826 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), so a(n) = 28.
%o A349826 (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 (n), n=m) ) } \\ _Rémy Sigrist_, Jan 02 2022
%Y A349826 Cf. A349824-A349827.
%K A349826 nonn
%O A349826 0,3
%A A349826 _N. J. A. Sloane_, Jan 01 2022
%E A349826 More terms from _Rémy Sigrist_, Jan 02 2022