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A070072 Number of distinct rectangles with integer sides <=n and squarefree area. 2
1, 2, 4, 4, 7, 9, 14, 14, 14, 17, 24, 24, 32, 37, 43, 43, 54, 54, 66, 66, 74, 83, 98, 98, 98, 108, 108, 108, 125, 133, 152, 152, 165, 178, 193, 193, 216, 231, 248, 248, 274, 285, 313, 313, 313, 331, 361, 361, 361, 361, 382, 382, 414 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, squarefree numbers.

FORMULA

a(n) = Sum_{i=1..n} Sum_{j= 1..i} mu(i*j)^2, where mu is the Moebius function (A008683). - Ridouane Oudra, Oct 17 2019

EXAMPLE

There are seven rectangles with sides <=5 having a squarefree area: 1 X 1, 1 X 2, 1 X 3, 1 X 5, 2 X 3, 2 X 5 and 3 X 5, whereas 1 X 4, 2 X 2, 2 X 4, 3 X 3, 3 X 4, 4 X 4, 4 X 5 and 5 X 5 are not squarefree; therefore a(5)=7.

PROG

(Haskell)

a070072 n = length [() | x <- [1..n], y <- [1..x], a008966 (x*y) == 1]

-- Reinhard Zumkeller, May 26 2012

(MAGMA) [&+[&+[MoebiusMu(i*j)^2:j in [1..i]]:i in [1..n]]:n in [1..53]]; // Marius A. Burtea, Oct 17 2019

CROSSREFS

Cf. A005117, A070073.

Cf. A008966, A008683.

Sequence in context: A340448 A241387 A284612 * A265259 A238493 A268781

Adjacent sequences:  A070069 A070070 A070071 * A070073 A070074 A070075

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 21 2002

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)