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A349827
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Iterate x -> A349824(x) starting at n; a(n) is the greatest term in the trajectory, or -1 if the trajectory increases for ever.
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3
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0, 1, 2, 3, 45, 5, 45, 7, 45, 27, 45, 11, 27, 13, 45, 50, 50, 17, 45, 19, 27, 27, 30, 23, 45, 27, 30, 27, 33, 29, 30, 31, 50, 33, 45, 45, 45, 37, 45, 50, 45, 41, 45, 43, 45, 45, 50, 47, 55, 49, 50, 51, 52, 53, 54, 55, 56, 57, 66, 59, 60, 61, 66, 63, 72, 65, 66
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refs;
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history;
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internal format)
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OFFSET
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0,3
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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).
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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, ..., ending at the loop (28, 33), and the high-point is 50, so a(16) = 50.
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PROG
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(PARI) a(n) = { my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=if (n==0, 0, my (f=factor(n)); bigomega(f)*sum(k=1, #f~, f[k, 1]*f[k, 2]))
); s[#s] } \\ Rémy Sigrist, Jan 01 2022
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CROSSREFS
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Cf. A349824-A349826.
Sequence in context: A334243 A323619 A349559 * A060415 A289661 A191996
Adjacent sequences: A349824 A349825 A349826 * A349828 A349829 A349830
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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 01 2022
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STATUS
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approved
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