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 A299352 For x=n, iterate the map x -> Product_{k is a prime dividing x} (k + (multiplicity of k)), a(n) is the number of steps to see a repeated term for the first time. 2
 3, 2, 1, 4, 3, 6, 5, 5, 5, 4, 3, 4, 3, 3, 3, 5, 4, 3, 2, 8, 4, 3, 2, 7, 11, 4, 8, 10, 9, 8, 7, 4, 6, 4, 3, 12, 11, 12, 10, 11, 10, 5, 4, 10, 9, 4, 3, 6, 9, 9, 12, 6, 5, 9, 11, 5, 2, 11, 10, 11, 10, 11, 6, 8, 11, 10, 9, 10, 11, 9, 8, 14, 13, 9, 5, 10, 13, 5, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS It appears that all n end in one of the orbits (6,12,16) or (20,24) or one the fixed points 4, 90, 120, verified to n=10^8. LINKS Lars Blomberg, Table of n, a(n) for n = 2..10000 EXAMPLE For n=2: 2=2^1 -> (2+1)=3=3^1 -> (3+1)=4=2^2 -> (2+2)=4; 4 is repeated so a(2)=3. For n=12: 12=2^2*3^1 -> (2+2)*(3+1)=16=2^4 -> (2+4)=6=2^1*3^1 -> (2+1)*(3+1)=12; 12 is repeated so a(12)=3. CROSSREFS Cf. A299351. Sequence in context: A327467 A077427 A107641 * A127671 A271724 A247641 Adjacent sequences:  A299349 A299350 A299351 * A299353 A299354 A299355 KEYWORD nonn AUTHOR Lars Blomberg, Feb 07 2018 STATUS approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)