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, 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

Author

Lars Blomberg, Feb 07 2018

Keywords

• nonn

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.

Examples

			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.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A008473 (the map), A299351.