%I #16 Jun 24 2020 16:57:09
%S 0,2,0,2,3,2,0,2,4,2,3,2,0,2,5,2,3,2,0,2,4,2,3,2,6,2,0,2,3,2,7,2,4,2,
%T 3,2,5,2,0,2,3,2,8,2,4,2,3,2,0,2,6,2,3,2,5,2,4,2,3,2,9,2,0,2,3,2,10,2,
%U 4,2,3,2,7,2,5,2,3,2,0,2,4,2,3,2,6,2
%N Flavius Josephus factor of n.
%C This sequence is analogous to the smallest prime factor of n. If n is a member of A000960, a(n) = 0, otherwise a(n) = the (k+1)-st step that rejects n from Flavius Josephus' sieve.
%C The n-values of records of this sequence are given by A100287 (see 2004 comment by Sloane).
%H Danny Rorabaugh, <a href="/A272800/b272800.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%o (Sage) # Function that returns an array of the first n terms.
%o def A272800(n):
%o A, B, k = [0]*n, range(n), 1
%o while k<len(B):
%o for i in range(floor(len(B)/(k + 1))):
%o A[B.pop(k*(i + 1))] = k + 1
%o k += 1
%o return A
%o # _Danny Rorabaugh_, May 13 2016
%Y Cf. A000960, A100002, A100287.
%K nonn
%O 1,2
%A _Max Barrentine_, May 06 2016