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A349825
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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).
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1
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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
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OFFSET
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0,5
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COMMENTS
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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).
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 0..10000
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A349824-A349827.
Sequence in context: A347688 A151949 A341486 * A320379 A308102 A338016
Adjacent sequences: A349822 A349823 A349824 * A349826 A349827 A349828
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 01 2022
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EXTENSIONS
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More terms from Rémy Sigrist, Jan 02 2022
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STATUS
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approved
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