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%I #11 Apr 19 2016 01:07:32
%S 1,1,1,3,1,7,1,10,4,7,1,33,1,7,9,28,1,39,1,33,9,7,1,133,4,7,15,33,1,
%T 91,1,80,9,7,9,229,1,7,9,133,1,91,1,33,53,7,1,474,4,39,9,33,1,175,9,
%U 133,9,7,1,569,1,7,53,208,9,91,1,33,9,91,1
%N Number of factorizations of (n,2*n) into pairs (k,l).
%C Pairs (k,l) must satisfy 0<k, 0<l; if k=1 then l=1. Definition of "*": (a,b)*(x,y)=(a*x,b*y); unit is (1,1).
%C Factorization is up to ordering of pairs, thus (2,2)*(5,10) is the same as (5,10)*(2,2). Factorizations may involve an arbitrary number of pairs, (2,2)*(3,4)*(5,6)=(30,48). - _Sean A. Irvine_, Mar 21 2013
%H Giovanni Resta, <a href="/A050521/b050521.txt">Table of n, a(n) for n = 1..1000</a>
%e (10,20) = (2,1)*(5,20) = (2,20)*(5*1) = (2,2)*(5,10) = (2,10)*(5,2) = (2,4)*(5,5) = (2,5)*(5,4); so a(10) = 7.
%Y Cf. A051707.
%K nonn,nice,easy
%O 1,4
%A _Yasutoshi Kohmoto_
%E More terms from _Sean A. Irvine_, Mar 21 2013