A303873 Total area of the family of squares with side length n such that n = p + q, p divides q and p < q.

0, 0, 9, 16, 25, 72, 49, 128, 162, 200, 121, 576, 169, 392, 675, 768, 289, 1296, 361, 1600, 1323, 968, 529, 3456, 1250, 1352, 2187, 3136, 841, 5400, 961, 4096, 3267, 2312, 3675, 9072, 1369, 2888, 4563, 9600, 1681, 10584, 1849, 7744, 10125, 4232, 2209, 18432

Offset

1,3

Links

Table of n, a(n) for n=1..48.

Index entries for sequences related to partitions

Formula

a(n) = n^2 * Sum_{i=1..floor((n-1)/2)} (floor((n-i)/i) - floor((n-i-1)/i)).

Mathematica

Table[n^2 * Sum[(Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 80}]

Prog

(Magma) [0, 0] cat [&+[(((n-k) div k)-(n-k-1) div k)*n^2: k in [1..(n-1) div 2]]: n in [3..80]]; // Vincenzo Librandi, May 02 2018

Crossrefs

Cf. A296955, A296966.

Sequence in context: A336449 A161183 A183345 * A257496 A351435 A369642

Adjacent sequences: A303870 A303871 A303872 * A303874 A303875 A303876

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 01 2018

Status

approved