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1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 4, 1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 2, 1, 3, 1, 5, 1, 2, 1, 1, 2, 4, 1, 1, 1, 3, 2, 1, 4, 1, 2, 3, 1, 5, 1, 1, 2, 1, 1, 2, 5, 1, 4, 1, 3, 1, 2, 1, 1, 2, 1, 1, 3, 6, 1, 2, 1, 5, 3, 1, 2, 1, 1, 4, 1, 6, 2, 1, 3, 1, 2, 1, 4, 3, 1, 1, 2, 1, 7, 1, 2, 1, 3, 1, 5, 1, 2, 1, 6, 1, 2, 1, 5, 1, 4, 1, 3, 2, 1
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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PROG
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(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
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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