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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.
3
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
OFFSET
2,1
COMMENTS
It appears that all n end in one of the orbits (6,12,16) or (20,24) or one of the fixed points 4, 90, 120, verified to n=10^8.
LINKS
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. A008473 (the map), A299351.
Sequence in context: A347832 A077427 A107641 * A127671 A271724 A247641
KEYWORD
nonn
AUTHOR
Lars Blomberg, Feb 07 2018
STATUS
approved