A349827 - OEIS

%I #11 Jan 02 2022 07:24:52

%S 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 27,30,27,33,29,30,31,50,33,45,45,45,37,45,50,45,41,45,43,45,45,50,47,

%U 55,49,50,51,52,53,54,55,56,57,66,59,60,61,66,63,72,65,66

%N 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 It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33).

%H Rémy Sigrist, <a href="/A349827/b349827.txt">Table of n, a(n) for n = 0..10000</a>

%e 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 (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 ); s[#s] } \\ _Rémy Sigrist_, Jan 01 2022

%Y Cf. A349824-A349826.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 01 2022

%E More terms from _Rémy Sigrist_, Jan 01 2022