A093411 - OEIS

%I #15 May 19 2021 10:27:07

%S 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 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 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 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 a(n) is odd for all positive n>0; a(n) = n iff n is odd.

%H Antti Karttunen, <a href="/A093411/b093411.txt">Table of n, a(n) for n = 0..40319</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F From _Antti Karttunen_, May 18 2021: (Start)

%F a(0) = 0, a(2n+1) = 2n+1, a(2n) = a(A076934(2n)).

%F a(n) = n / A329379(n).

%F (End)

%e a(18) = 3, 18/6 = 3. though 18/2 = 9.

%t 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 (PARI)

%o A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));

%o A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n)))); \\ _Antti Karttunen_, May 18 2021

%Y For bisection see A109375, for positions of ones, A344181.

%Y Cf. A000142, A076934, A329379.

%Y Cf. also A328478.

%K easy,nonn

%O 0,4

%A _Amarnath Murthy_, Mar 30 2004

%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 25 2005

%E Definition further clarified by _Antti Karttunen_, May 18 2021