%I A066446
%S A066446 0,1,1,3,1,6,1,6,3,6,1,15,1,6,6,10,1,15,1,15,6,6,1,28,3,6,6,15,1,28,1,
%T A066446 15,6,6,6,36,1,6,6,28,1,28,1,15,15,6,1,45,3,15,6,15,1,28,6,28,6,6,1,66,
%U A066446 1,6,15,21,6,28,1,15,6,28,1,66,1,6,15,15,6,28,1,45,10,6,1,66,6,6,6,28
%N A066446 Number of unordered divisor pairs of n.
%C A066446 a(n) = 1 iff n is a prime.
%F A066446 Combinations of d(n), the number of divisors of n (A000005), taken two 
               at a time. If the canonical factorization of n into prime powers 
               is Product p^e(p) then d(n) = Product (e(p) + 1). Therefore C( d(n), 
               2) = d(n)*{ d(n)-1 }/2 which is a triangular number (A000217).
%e A066446 The divisors of 6 are 1, 2, 3 & 6. In unordered pairs they are {1, 2}, 
               {1, 3}, {1, 6}, {2, 3}, {2, 6}, & {3, 6}. Since there are six pairs, 
               a(6) = 6. Also d(6) = 4. 4*3/2 = 6.
%t A066446 Table[ Binomial[ DivisorSigma[0, n], 2], {n, 1, 100}]
%Y A066446 Cf. A000005, A000217, A129510.
%Y A066446 Sequence in context: A068436 A019570 A040011 this_sequence A069625 A111614 
               A076889
%Y A066446 Adjacent sequences: A066443 A066444 A066445 this_sequence A066447 A066448 
               A066449
%K A066446 easy,nonn
%O A066446 1,4
%A A066446 Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 28 2001