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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.
7
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, 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, 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
OFFSET
0,4
COMMENTS
a(n) is odd for all positive n>0; a(n) = n iff n is odd.
FORMULA
From Antti Karttunen, May 18 2021: (Start)
a(0) = 0, a(2n+1) = 2n+1, a(2n) = a(A076934(2n)).
a(n) = n / A329379(n).
(End)
EXAMPLE
a(18) = 3, 18/6 = 3. though 18/2 = 9.
MATHEMATICA
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 *)
PROG
(PARI)
A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
A093411(n) = if(!n, n, if(n%2, n, A093411(A076934(n)))); \\ Antti Karttunen, May 18 2021
CROSSREFS
For bisection see A109375, for positions of ones, A344181.
Cf. also A328478.
Sequence in context: A336898 A300330 A328478 * A147088 A346468 A340083
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Mar 30 2004
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Aug 25 2005
Definition further clarified by Antti Karttunen, May 18 2021
STATUS
approved