A349827 Iterate x -> A349824(x) starting at n; a(n) is the greatest term in the trajectory, or -1 if the trajectory increases for ever.

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, 27, 30, 27, 33, 29, 30, 31, 50, 33, 45, 45, 45, 37, 45, 50, 45, 41, 45, 43, 45, 45, 50, 47, 55, 49, 50, 51, 52, 53, 54, 55, 56, 57, 66, 59, 60, 61, 66, 63, 72, 65, 66

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), and the high-point is 50, so a(16) = 50.

Prog

(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]))
); s[#s] } \\ Rémy Sigrist, Jan 01 2022

Crossrefs

Cf. A349824-A349826.

Sequence in context: A334243 A323619 A349559 * A060415 A289661 A191996

Adjacent sequences: A349824 A349825 A349826 * A349828 A349829 A349830

Keyword

nonn

Author

N. J. A. Sloane, Jan 01 2022

Extensions

More terms from Rémy Sigrist, Jan 01 2022

Status

approved