%I #12 Apr 08 2020 02:27:39
%S 0,0,0,1,1,1,1,4,3,4,4,5,5,5,5,11,11,9,9,12,9,12,12,15,16,15,17,16,16,
%T 16,16,26,16,26,17,24,24,24,24,30,30,25,25,31,27,31,31,37,31,38,37,38,
%U 38,40,39,41,40,41,41,42,42,42,43,57,43,43,43,58,43,46,46,57,57,57,54,58,47,58,58,68,66,68,68,62,69,62,62,72,72
%N Number of integers in range 1..n that are not encountered on any of the possible paths from n to 1 when iterating with nondeterministic map k > k  k/p, where p is any prime factor of k.
%H Antti Karttunen, <a href="/A332810/b332810.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = n  A332809(n).
%e a(12): we have three alternative paths: {12, 8, 4, 2, 1}, {12, 6, 4, 2, 1} or {12, 6, 3, 2, 1}, with [5, 7, 9, 10, 11] being the only numbers in range 1..12 that do not occur in any of those paths, therefore a(12) = 5.
%o (PARI)
%o up_to = 105;
%o A332809list(up_to) = { my(v=vector(up_to)); v[1] = Set([1]); for(n=2,up_to, my(f=factor(n)[, 1]~, s=Set([n])); for(i=1,#f,s = setunion(s,v[n(n/f[i])])); v[n] = s); apply(length,v); }
%o v332809 = A332809list(up_to);
%o A332810(n) = (nv332809[n]);
%Y Cf. A064097, A332809, A333123.
%K nonn
%O 1,8
%A _Antti Karttunen_, Apr 04 2020
