%I A100073
%S A100073 0,0,1,0,1,0,1,1,1,0,1,1,1,0,2,1,1,0,1,1,2,0,1,2,1,0,2,1,1,0,1,2,2,0,2,
%T A100073 1,1,0,2,2,1,0,1,1,3,0,1,3,1,0,2,1,1,0,2,2,2,0,1,2,1,0,3,2,2,0,1,1,2,0,
%U A100073 1,3,1,0,3,1,2,0,1,3,2,0,1,2,2,0,2,2,1,0,2,1,2,0,2,4,1,0,3,1,1,0,1,2,4
%N A100073 Number of representations of n as the difference of two positive squares.
%C A100073 Note that for odd n, a(n) = 1 iff n is a prime, or a prime squared.
%F A100073 a(n) = A056924(n) for odd n, a(n) = A056924(n/4) if 4|n, otherwise a(n) 
               = 0.
%e A100073 a(15) = 2 because 15 = 16-1 = 64-49.
%t A100073 nn=150; a=Table[0, {nn}]; Do[y=x-1; While[d=x^2-y^2; d<=nn&&y>0, a[[d]]++; 
               y-- ], {x, 1+nn/2}]; a
%Y A100073 Cf. A056924 (number of divisors of n that are less than sqrt(n)), A016825 
               (numbers not the difference of two squares), A034178 (number of representations 
               of n as the difference of two squares).
%Y A100073 Sequence in context: A026920 A060763 A131576 this_sequence A075685 A037906 
               A120936
%Y A100073 Adjacent sequences: A100070 A100071 A100072 this_sequence A100074 A100075 
               A100076
%K A100073 easy,nonn
%O A100073 1,15
%A A100073 T. D. Noe (noe(AT)sspectra.com), Nov 02 2004