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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.
3
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 01 2022
EXTENSIONS
More terms from Rémy Sigrist, Jan 02 2022
STATUS
approved