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 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 (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), 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. A349824-A349827. 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

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)