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

1,4

Links

Table of n, a(n) for n=1..78.

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

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.

Example

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).

Crossrefs

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

Sequence in context: A274473 A280526 A335552 * A095660 A290080 A289617

Adjacent sequences: A306838 A306839 A306840 * A306842 A306843 A306844

Keyword

nonn

Author

Freddy Barrera, Mar 12 2019

Status

approved