A303221 Total area of all rectangles with dimensions p and p + q such that p and q are both squarefree, n = p + q and p <= q.

0, 2, 3, 12, 10, 24, 21, 48, 45, 80, 66, 168, 143, 154, 120, 272, 306, 288, 247, 640, 525, 594, 437, 936, 800, 1014, 945, 1624, 1160, 1410, 992, 1952, 1551, 2210, 1435, 3348, 2146, 2546, 2106, 3800, 2993, 3360, 3827, 5720, 4905, 4324, 4089, 6816, 5390, 5300

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Index entries for sequences related to partitions

Formula

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

a(n) = n * A261985(n). - Wesley Ivan Hurt, Jan 05 2024

Mathematica

Table[n*Sum[i*MoebiusMu[i]^2 MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 80}]

Prog

(Magma) [0] cat [&+[n*k*MoebiusMu(k)^2*MoebiusMu(n-k)^2: k in [1..Floor(n/2)]]: n in [2..60]]; // Vincenzo Librandi, Apr 21 2018
(PARI) a(n) = n * sum(i=1, n\2, i * moebius(i)^2 * moebius(n-i)^2); \\ Michel Marcus, Apr 21 2018

Crossrefs

Cf. A008683, A261985.

Sequence in context: A075711 A079077 A027611 * A345049 A168059 A068550

Adjacent sequences: A303218 A303219 A303220 * A303222 A303223 A303224

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 19 2018

Status

approved