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 A349825 Number of steps when x -> A349824(x) is iterated starting at n needed to reach fixed point or 28, or -1 if trajectory increases for ever or ends in a nontrivial loop other than (28,33). 1
 0, 1, 0, 0, 9, 0, 10, 0, 8, 4, 9, 0, 3, 0, 8, 9, 8, 0, 7, 0, 1, 2, 2, 0, 6, 2, 1, 0, 0, 0, 0, 0, 7, 1, 8, 7, 5, 0, 7, 8, 4, 0, 6, 0, 3, 2, 7, 0, 9, 1, 6, 5, 6, 0, 4, 8, 7, 4, 12, 0, 10, 0, 11, 9, 12, 6, 10, 0, 10, 7, 7, 0, 11, 0, 6, 9, 8, 6, 5, 0, 7, 10, 9, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33). a(n) = number of steps to reach A349826(n) (or -1). 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, ..., reaching low point of 28 after 8 steps, so a(16) = 8. 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 (k), n=m) ) } \\ Rémy Sigrist, Jan 02 2022 CROSSREFS Cf. A349824-A349827. Sequence in context: A347688 A151949 A341486 * A320379 A308102 A338016 Adjacent sequences: A349822 A349823 A349824 * A349826 A349827 A349828 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 01 2022 EXTENSIONS More terms from Rémy Sigrist, Jan 02 2022 STATUS approved

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Last modified February 1 12:28 EST 2023. Contains 359993 sequences. (Running on oeis4.)