OFFSET
1,4
COMMENTS
The sequence measures, in a sense, inversions in remainders of odd numbers upon factoring out their largest divisors (see A281680).
In A281680, we have A281680(4) = A281680(7) = A281680(10) = 3 (and there will be infinitely many 1's to the right after each one of them), so there is why a(1)=a(2)=a(3)=1. Then we have A281680(12) = 5 (and there will be infinitely many 1's and 3's to the right), so that's why a(4) = 2, and so forth. I used 1,2,3,... here to represent these inversions, but any other symbols could have been used.
Entries correspond to the position of the lowest prime factor of the odd composites, with prime=3 being position 1. - Bill McEachen, Jan 28 2018
LINKS
Bill McEachen, Table of n, a(n) for n = 1..10000
PROG
(PARI) genit(maxx)={forcomposite(i5=9, maxx, if(i5%2==0, next); ptr=0; forprime(x=3, maxx, ptr+=1; if(i5%x==0, print1(ptr, ", "); break))); } \\ Bill McEachen, Jan 28 2018
(Python)
from sympy import primepi, primefactors
def A281681(n):
if n == 1: return 1
m, k = n, primepi(n) + n + (n>>1)
while m != k:
m, k = k, primepi(k) + n + (k>>1)
return primepi(min(primefactors(m)))-1 # Chai Wah Wu, Aug 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jan 26 2017
EXTENSIONS
Name changed by Robert Israel, Aug 03 2020
STATUS
approved