[seqfan] A conjecture for composite numbers

[Vladimir Shevelev]

Let n be a composite number with prime power factorization n=prime(1)^c_1*prime(2)^c_2*...*prime(k)^c_k. 
Let f_1(n)=n+c_1+c_2+...+c_k - 1. Conjecture. A finite iteration of  f_1 leads to a prime.
Example. Let n=60. Then f_1=63, f_2=65, f_3=66, f_4=68, f_5=70, f_6=72, f_7=76, f_8=78, f_9=80, f_10=84, f_11=87, f_12=88, f_13=91, f_14=92, f_15=94, f_16=95, f_17=96, f_18=101  (I submitted sequence A213980).
 
Are there any thoughts to prove it? Or the difficulty of it is close to 3n+1 problem?
 
Regards,
Vladimir

 Shevelev Vladimir‎