cp's OEIS Frontend

A332810 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.

%I A332810 #12 Apr 08 2020 02:27:39
%S A332810 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 A332810 16,16,26,16,26,17,24,24,24,24,30,30,25,25,31,27,31,31,37,31,38,37,38,
%U A332810 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 A332810 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 A332810 Antti Karttunen, <a href="/A332810/b332810.txt">Table of n, a(n) for n = 1..20000</a>
%F A332810 a(n) = n - A332809(n).
%e A332810 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 A332810 (PARI)
%o A332810 up_to = 105;
%o A332810 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 A332810 v332809 = A332809list(up_to);
%o A332810 A332810(n) = (n-v332809[n]);
%Y A332810 Cf. A064097, A332809, A333123.
%K A332810 nonn
%O A332810 1,8
%A A332810 _Antti Karttunen_, Apr 04 2020