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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

%I

%S 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,

%T 27,30,27,28,29,30,31,28,28,28,28,28,37,28,28,28,41,28,43,28,28,28,47,

%U 28,28,28,28,28,53,28,28,28,28,28,59,28,61,28,28,28,28,28

%N 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.

%C It is conjectured that every trajectory eventually reaches one of the fixed points {primes union 0, 27, 30} or the loop (28, 33).

%H Rémy Sigrist, <a href="/A349826/b349826.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%o (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

%Y Cf. A349824-A349827.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 01 2022

%E More terms from _Rémy Sigrist_, Jan 02 2022

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Last modified February 3 12:01 EST 2023. Contains 360034 sequences. (Running on oeis4.)