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

0,5

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).

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A349824-A349827.

Sequence in context: A347688 A151949 A341486 * A320379 A308102 A338016

Adjacent sequences: A349822 A349823 A349824 * A349826 A349827 A349828

Keyword

nonn

Author

N. J. A. Sloane, Jan 01 2022

Extensions

More terms from Rémy Sigrist, Jan 02 2022

Status

approved