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.

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, 27, 30, 27, 28, 29, 30, 31, 28, 28, 28, 28, 28, 37, 28, 28, 28, 41, 28, 43, 28, 28, 28, 47, 28, 28, 28, 28, 28, 53, 28, 28, 28, 28, 28, 59, 28, 61, 28, 28, 28, 28, 28

Offset

0,3

Comments

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

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, ..., ending at the loop (28, 33), so a(n) = 28.

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 (n), n=m) ) } \\ Rémy Sigrist, Jan 02 2022

Crossrefs

Cf. A349824-A349827.

Sequence in context: A059089 A098812 A073049 * A279880 A279140 A279755

Adjacent sequences: A349823 A349824 A349825 * A349827 A349828 A349829

Keyword

nonn

Author

N. J. A. Sloane, Jan 01 2022

Extensions

More terms from Rémy Sigrist, Jan 02 2022

Status

approved