%I #5 Aug 26 2015 12:44:51

%S 0,1,1,3,1,5,1,6,3,6,1,10,1,6,5,10,1,13,1,13,6,6,1,18,3,6,6,14,1,19,1,

%T 15,6,6,6,24,1,6,6,22,1,23,1,15,12,6,1,30,3,15,6,15,1,25,6,23,6,6,1,

%U 37,1,6,13,21,6,25,1,15,6,24,1,40,1,6,13,15,6,26,1,34,10,6,1,45,6,6,6,26

%N Number of distinct differences between pairs of distinct divisors of n.

%C a(n) = #{|x-y|: x <> y and n mod x = n mod y = 0};

%C a(n) = 1 iff n is prime;

%C a(n) <= A000217(A000005(a(n))-1) = A066446(n):

%C a(A129511(n))=A066446(A129511(n)), a(A129512(n)) < A066446(A129512(n)).

%H Charles R Greathouse IV, <a href="/A129510/b129510.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Divisor.html">Divisor</a>

%e n=44, set of divisors of 44 = {1,2,4,11,22,44}:

%e 44-22=22, 44-11=33, 44-4=40, 44-2=42, 44-1=41,

%e 22-11=11, 22-4=18, 22-2=20, 22-1=21,

%e 11-4=7, 11-2=9, 11-1=10, 4-2=2, 4-1=3, 2-1=1,

%e a(44) = #{1,2,3,7,9,10,11,18,20,21,22,33,40,41,42} = 15;

%e n=45, set of divisors of 45 = {1,3,5,9,15,45}:

%e 45-15=30, 45-9=36, 45-5=40, 45-3=42, 45-1=44,

%e 15-9=6, 15-5=10, 15-3=12, 15-1=14,

%e 9-5=4, 9-3=6, 9-1=8, 5-3=2, 5-1=4, 3-1=2,

%e a(45) = #{2,4,6,8,10,12,14,30,36,40,42,44} = 12.

%o (PARI) a(n)=my(d=divisors(n),v=List()); for(i=1,#d-1,for(j=i+1,#d, listput(v,d[j]-d[i]))); #Set(v) \\ _Charles R Greathouse IV_, Aug 26 2015

%Y Cf. A000005.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Apr 19 2007