login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A334361 Number of r X s rectangles with squarefree side lengths such that r < s, r + s = 2n and r | s. 1
0, 1, 1, 2, 0, 2, 1, 2, 2, 2, 1, 3, 0, 2, 1, 2, 1, 4, 1, 4, 3, 3, 0, 3, 0, 2, 2, 2, 1, 4, 1, 1, 2, 3, 2, 4, 1, 2, 2, 3, 0, 5, 1, 4, 3, 2, 1, 3, 2, 1, 2, 4, 1, 4, 2, 3, 3, 3, 0, 6, 0, 3, 3, 1, 1, 4, 1, 3, 2, 5, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..90.

FORMULA

a(n) = Sum_{i=1..n-1} (1 - ceiling((2*n-i)/i) + floor((2*n-i)/i)) * mu(i)^2 * mu(2*n-i)^2, where mu is the Möbius function (A008683).

EXAMPLE

a(12) = 3; 2*12 = 24 has 3 rectangles with squarefree side lengths, 1 X 23, 2 X 22 and 3 X 21 such that 1 | 23, 2 | 22 and 3 | 21.

MATHEMATICA

Table[Sum[MoebiusMu[i]^2 MoebiusMu[2 n - i]^2 (1 - Ceiling[(2 n - i)/i] + Floor[(2 n - i)/i]), {i, n - 1}], {n, 100}]

CROSSREFS

Cf. A008683, A327567.

Sequence in context: A319514 A141454 A301564 * A219791 A029345 A153149

Adjacent sequences:  A334358 A334359 A334360 * A334362 A334363 A334364

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 24 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 15:00 EDT 2021. Contains 343116 sequences. (Running on oeis4.)