A303205 Number of rectangles with squarefree area and dimensions p and |q-p| such that n = p + q and p < q.

0, 0, 1, 1, 2, 0, 3, 2, 2, 0, 3, 2, 4, 0, 3, 4, 6, 0, 5, 2, 4, 0, 7, 4, 6, 0, 6, 4, 7, 0, 8, 6, 7, 0, 6, 6, 9, 0, 8, 6, 12, 0, 13, 8, 9, 0, 12, 8, 11, 0, 9, 8, 13, 0, 9, 6, 12, 0, 15, 8, 16, 0, 12, 10, 12, 0, 17, 12, 13, 0, 18, 10, 20, 0, 14, 12, 15, 0, 21

Offset

1,5

Links

Table of n, a(n) for n=1..79.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Prog

(Magma) [0, 0] cat [&+[MoebiusMu(k*(n-2*k))^2: k in [1..((n-1) div 2)]]: n in [3..80]]; // Vincenzo Librandi, Apr 21 2018
(PARI) a(n) = sum(i=1, (n-1)\2, moebius(i*(n-2*i))^2); \\ Michel Marcus, Apr 21 2018

Crossrefs

Cf. A008683, A303165.

Sequence in context: A090722 A221879 A171934 * A082785 A100949 A152164

Adjacent sequences: A303202 A303203 A303204 * A303206 A303207 A303208

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 19 2018

Status

approved