%I #14 Aug 19 2014 01:01:01

%S 0,0,1,1,2,0,3,2,1,2,3,1,3,1,1,2,5,2,3,2,1,2,3,1,4,2,3,4,3,0,3,4,3,2,

%T 3,0,3,4,3,1,2,2,5,2,3,4,5,2,3,2,1,3,4,0,3,2,3,4,5,3,4,3,2,2,3,2,5,2,

%U 1,2,5,4,5,2,1,2,5,2,3,4,3,3,4,1,4,2,3,4,3,0,3,4,5,4,3,0

%N Number of prime anti-divisors m of n.

%C The maximum value of a(n) is 9 for 1 <= n <= 10000.

%C There are 167 instances of a(n) = 0 for 1 <= n <= 10000 (See A241557).

%H Michael De Vlieger, <a href="/A241556/b241556.txt">Table of n, a(n) for n = 1..10000</a>

%e a(10) = 2, since 10 has 3 anti-divisors {3, 4, 7}; only {3, 7} are prime.

%e a(9223) = 9; these are {2, 3, 5, 7, 11, 13, 17, 31, 43}.

%t primeAntiDivisors[n_] := Select[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)], PrimeQ]; a241556[n_Integer] := Map[Length[primeAntiDivisors[#]] &, Range[n]]; a241556[120]

%Y Cf. A066272, A192281, A242965, A242966, A241557.

%K nonn

%O 1,5

%A _Michael De Vlieger_, Aug 08 2014