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 A349827 Iterate x -> A349824(x) starting at n; a(n) is the greatest term in the trajectory, or -1 if the trajectory increases for ever. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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), and the high-point is 50, so a(16) = 50. PROG (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 CROSSREFS Cf. A349824-A349826. Sequence in context: A334243 A323619 A349559 * A060415 A289661 A191996 Adjacent sequences: A349824 A349825 A349826 * A349828 A349829 A349830 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 01 2022 EXTENSIONS More terms from Rémy Sigrist, Jan 01 2022 STATUS approved

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Last modified May 29 13:20 EDT 2023. Contains 363042 sequences. (Running on oeis4.)