1,4

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

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

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.

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).

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

Sequence in context: A201662 A274473 A280526 * A095660 A290080 A289617

Adjacent sequences: A306838 A306839 A306840 * A306842 A306843 A306844

nonn

Freddy Barrera, Mar 12 2019

approved