

A303221


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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(ni)^2, where mu is the Möbius function (A008683).


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(nk)^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(ni)^2); \\ Michel Marcus, Apr 21 2018


CROSSREFS

Cf. A008683, A261985.
Sequence in context: A075711 A079077 A027611 * A168059 A068550 A093432
Adjacent sequences: A303218 A303219 A303220 * A303222 A303223 A303224


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 19 2018


STATUS

approved



