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

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).

Examples

			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.
		

Links

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

Crossrefs

Cf. A349824-A349826.

Programs

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

Extensions

More terms from Rémy Sigrist, Jan 01 2022