login
The defining property of the sequences {A, B} = {A000028, A000379} is that they are the unique pair of sets complementary with respect to the positive integers such that p(n) = |{x : x, y in A, x < y, xy = n}| = |{x : x, y in B, x < y, xy = n}| for all n >= 1. The present sequence gives the values of p(n).
4

%I #8 Feb 22 2013 21:38:14

%S 0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,

%T 1,1,0,1,1,0,0,0,0,1,1,1,0,2,0,1,1,1,0,0,1,0,1,1,0,1,0,1,1,1,1,0,0,1,

%U 1,0,0,1,0,1,1,1,1,0,0,2,0,1,0,1,1,1,1,0,0,1,1,1,1,1,1,1,0,1,1

%N The defining property of the sequences {A, B} = {A000028, A000379} is that they are the unique pair of sets complementary with respect to the positive integers such that p(n) = |{x : x, y in A, x < y, xy = n}| = |{x : x, y in B, x < y, xy = n}| for all n >= 1. The present sequence gives the values of p(n).

%H David W. Wilson, <a href="/A133008/b133008.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a133008 n = length [x | x <- takeWhile (< n) a000028_list,

%o n `mod` x == 0, let y = n `div` x, x < y,

%o y `elem` takeWhile (<= n) a000028_list]

%o -- _Reinhard Zumkeller_, Oct 05 2011

%Y Cf. A000028, A000379, A000069, A001969, A133009.

%K nonn

%O 1,48

%A _David W. Wilson_, Dec 21 2007