OFFSET
2,1
COMMENTS
It appears that all n end in the orbit (3,4) or the fixed point 12, verified to n=10^8.
Let p,q,r,... be primes that increased by 1 become a power of 2 (the Mersenne primes, A000668). Then for n = p^a*q^b*r^c*..., a,b,c,...>=1 -> (p+1)*(q+1)*(r+1)... = 2^e, e>=2 -> (2+1)=3.
The case 3^k, k>=2 first yields 4 and then 3: -> (3+1)=4=2^2 -> (2+1)=3.
It appears that these are the only ones entering the orbit (3,4), all other n end in the fixed point 12.
LINKS
Lars Blomberg, Table of n, a(n) for n = 2..10000
EXAMPLE
For n=2: 2 -> (2+1)=3 -> (3+1)=4=2^2 -> (2+1)=3; 3 is repeated so a(2)=3.
For n=19: 19 -> (19+1)=20=2^2*5 -> (2+1)*(5+1)=18=2*3^2 -> (2+1)*(3+1)=12=2^2*3 -> (2+1)*(3+1)=12; 12 is repeated so a(19)=4.
CROSSREFS
KEYWORD
nonn
AUTHOR
Lars Blomberg, Feb 07 2018
STATUS
approved