A349825 - OEIS

%I #9 Jan 02 2022 07:24:40

%S 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 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 10,0,10,7,7,0,11,0,6,9,8,6,5,0,7,10,9,0

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

%C a(n) = number of steps to reach A349826(n) (or -1).

%H Rémy Sigrist, <a href="/A349825/b349825.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, ..., reaching low point of 28 after 8 steps, so a(16) = 8.

%o (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 Cf. A349824-A349827.

%K nonn

%O 0,5

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

%E More terms from _Rémy Sigrist_, Jan 02 2022