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).

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

Offset: 0

Author

N. J. A. Sloane, Jan 01 2022

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A349824-A349827.

Programs

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

Extensions

More terms from Rémy Sigrist, Jan 02 2022