

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
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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: A347832 A077427 A107641 * A127671 A271724 A247641
Adjacent sequences: A299349 A299350 A299351 * A299353 A299354 A299355


KEYWORD

nonn


AUTHOR

Lars Blomberg, Feb 07 2018


STATUS

approved



