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A093411 Divide n by the largest factorial that divides it and repeat until an odd number is reached, which will be the result; a(0) = 0.

%I A093411 #15 May 19 2021 10:27:07
%S A093411 0,1,1,3,1,5,1,7,1,9,5,11,1,13,7,15,1,17,3,19,5,21,11,23,1,25,13,27,7,
%T A093411 29,5,31,1,33,17,35,1,37,19,39,5,41,7,43,11,45,23,47,1,49,25,51,13,53,
%U A093411 9,55,7,57,29,59,5,61,31,63,1,65,11,67,17,69,35,71,3,73,37,75,19,77,13,79
%N A093411 Divide n by the largest factorial that divides it and repeat until an odd number is reached, which will be the result; a(0) = 0.
%C A093411 a(n) is odd for all positive n>0; a(n) = n iff n is odd.
%H A093411 Antti Karttunen, <a href="/A093411/b093411.txt">Table of n, a(n) for n = 0..40319</a>
%H A093411 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A093411 From _Antti Karttunen_, May 18 2021: (Start)
%F A093411 a(0) = 0, a(2n+1) = 2n+1, a(2n) = a(A076934(2n)).
%F A093411 a(n) = n / A329379(n).
%F A093411 (End)
%e A093411 a(18) = 3, 18/6 = 3. though 18/2 = 9.
%t A093411 f[n_] := Block[{m = n, k = n}, While[k > 1, While[ IntegerQ[m/k! ], m = m/k! ]; k-- ]; m]; Table[ f[n], {n, 0, 79}] (* _Robert G. Wilson v_ *)
%o A093411 (PARI)
%o A093411 A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
%o A093411 A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n)))); \\ _Antti Karttunen_, May 18 2021
%Y A093411 For bisection see A109375, for positions of ones, A344181.
%Y A093411 Cf. A000142, A076934, A329379.
%Y A093411 Cf. also A328478.
%K A093411 easy,nonn
%O A093411 0,4
%A A093411 _Amarnath Murthy_, Mar 30 2004
%E A093411 Edited, corrected and extended by _Robert G. Wilson v_, Aug 25 2005
%E A093411 Definition further clarified by _Antti Karttunen_, May 18 2021