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 A281681 a(n) = A055396(A071904(n))-1. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 CROSSREFS Cf. A055396, A071904, A281680, A162022. Sequence in context: A359236 A320010 A210763 * A218799 A078770 A072038 Adjacent sequences: A281678 A281679 A281680 * A281682 A281683 A281684 KEYWORD nonn AUTHOR Enrique Navarrete, Jan 26 2017 EXTENSIONS Name changed by Robert Israel, Aug 03 2020 STATUS approved

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)