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Number of factorizations of (n,n) into pairs (i,j) with i,j>1.
2

%I #2 Mar 30 2012 17:37:15

%S 1,1,1,2,1,3,1,4,2,3,1,11,1,3,3,9,1,11,1,11,3,3,1,35,2,3,4,11,1,25,1,

%T 20,3,3,3,55,1,3,3,35,1,25,1,11,11,3,1,106,2,11,3,11,1,35,3,35,3,3,1,

%U 132,1,3,11,45,3,25,1,11,3,25,1,222,1,3,11,11,3,25,1,106,9,3,1,132,3,3

%N Number of factorizations of (n,n) into pairs (i,j) with i,j>1.

%C (a,b)*(x,y)=(a*x,b*y).

%C a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^3*3 and 375=3*5^3 both have prime signature (3,1).

%Y Cf. A108461. Main diagonal of A108465. a(A025487)=A108467. a(p^k)=A108469(k). a(A002110)=A023997.

%K nonn

%O 1,4

%A _Christian G. Bower_, Jun 03 2005