A348161 Number of factorizations of (n,n) into one or two pairs (i,j) with i > 0, j > 0 (and if i=1 then j=1).

1, 1, 1, 3, 1, 5, 1, 5, 3, 5, 1, 13, 1, 5, 5, 9, 1, 13, 1, 13, 5, 5, 1, 25, 3, 5, 5, 13, 1, 25, 1, 13, 5, 5, 5, 33, 1, 5, 5, 25, 1, 25, 1, 13, 13, 5, 1, 41, 3, 13, 5, 13, 1, 25, 5, 25, 5, 5, 1, 61, 1, 5, 13, 19, 5, 25, 1, 13, 5, 25, 1, 61, 1, 5, 13, 13, 5, 25

Offset: 1

Author

Sean A. Irvine, Oct 03 2021

Keywords

• nonn

Examples

			(4,4) = (2,4)*(2,1) = (2,2)*(2,2), so a(4)=3.
		

Crossrefs

Main diagonal of A348157.

Cf. A051707 (any number of pairs).

Formula

For n > 1, a(n) = ceiling((tau(n)-2)*tau(n)/2) + 1, where tau(n) = A000005(n).