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A303385 Total area of the family of rectangles with dimensions p and q such that p divides q, n = p + q and p < q. 3
0, 0, 2, 3, 4, 13, 6, 19, 26, 25, 10, 90, 12, 37, 100, 91, 16, 166, 18, 194, 172, 61, 22, 446, 124, 73, 260, 322, 28, 635, 30, 395, 364, 97, 380, 1041, 36, 109, 484, 990, 40, 1091, 42, 650, 1144, 133, 46, 1966, 342, 770, 772, 850, 52, 1651, 788, 1686, 940 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

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

PROG

(MAGMA) [0, 0] cat [&+[k*(n-k)*(((n-k) div k)-((n-k-1) div k)):  k in [1..(n-1) div 2]]: n in [3..80]]; // Vincenzo Librandi, Apr 23 2018

CROSSREFS

Cf. A303384.

Sequence in context: A276530 A251411 A117342 * A325709 A126129 A102947

Adjacent sequences:  A303382 A303383 A303384 * A303386 A303387 A303388

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 22 2018

STATUS

approved

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Last modified August 19 08:36 EDT 2019. Contains 326115 sequences. (Running on oeis4.)