

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

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. A349824A349827.
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



