

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
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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



EXTENSIONS



STATUS

approved



