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A306841 Number of rectangles of integer sides whose area or perimeter is n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A201662 A274473 A280526 * A095660 A290080 A289617

Adjacent sequences:  A306838 A306839 A306840 * A306842 A306843 A306844

KEYWORD

nonn

AUTHOR

Freddy Barrera, Mar 12 2019

STATUS

approved

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Last modified September 17 08:56 EDT 2019. Contains 327127 sequences. (Running on oeis4.)