A303115 Total area of the family of rectangles with side lengths p and q such that n = p + q, p < q, and |q-p| is not semiprime.

0, 0, 2, 3, 10, 8, 28, 15, 60, 33, 100, 55, 160, 94, 244, 139, 340, 207, 466, 302, 626, 428, 802, 566, 1018, 741, 1252, 930, 1532, 1162, 1862, 1441, 2246, 1771, 2654, 2121, 3086, 2528, 3580, 2957, 4100, 3449, 4688, 4008, 5348, 4638, 6084, 5296, 6900, 6031

Offset

1,3

Links

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

Index entries for sequences related to partitions

Formula

a(n) = Sum_{1..floor((n-1)/2)} i * (n-i) * (1 - [Omega(n-2i) = 2]), where [] is the Iverson bracket and Omega = A001222.

Mathematica

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

Crossrefs

Cf. A001222, A303110.

Sequence in context: A278561 A369991 A193729 * A074068 A351413 A283436

Adjacent sequences: A303112 A303113 A303114 * A303116 A303117 A303118

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 18 2018

Status

approved