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

2,1

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

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. A008473 (the map), A299351.

Sequence in context: A347832 A077427 A107641 * A127671 A271724 A247641

Adjacent sequences: A299349 A299350 A299351 * A299353 A299354 A299355

Keyword

nonn

Author

Lars Blomberg, Feb 07 2018

Status

approved