A306841 Number of rectangles of integer sides whose area or perimeter is n.

1, 1, 1, 3, 1, 3, 1, 4, 2, 4, 1, 6, 1, 5, 2, 7, 1, 7, 1, 8, 2, 7, 1, 10, 2, 8, 2, 10, 1, 11, 1, 11, 2, 10, 2, 14, 1, 11, 2, 14, 1, 14, 1, 14, 3, 13, 1, 17, 2, 15, 2, 16, 1, 17, 2, 18, 2, 16, 1, 21, 1, 17, 3, 20, 2, 20, 1, 20, 2, 21, 1, 24, 1, 20, 3, 22, 2, 23

Offset: 1

Author

Freddy Barrera, Mar 12 2019

Keywords

• nonn

Examples

			a(4) = 3 because there are two rectangles of integer sides of area 4 (2 X 2 and 1 X 4) and one rectangle of integer sides of perimeter 4 (1 X 1).
		

Links

• MathOverflow, Tiling a square with rectangles whose areas or perimeters are 1, 2, 3, ..., N

Crossrefs

Cf. A038548 (area n), A004526 (perimeter 2n).

Formula

a(n) = ceiling(d(n)/2) + floor(n/4) if n is even, a(n) = ceiling(d(n)/2) otherwise, where d(n) is the number of divisors of n.