A303115 - OEIS

%I #6 Jun 20 2019 04:27:09

%S 0,0,2,3,10,8,28,15,60,33,100,55,160,94,244,139,340,207,466,302,626,

%T 428,802,566,1018,741,1252,930,1532,1162,1862,1441,2246,1771,2654,

%U 2121,3086,2528,3580,2957,4100,3449,4688,4008,5348,4638,6084,5296,6900,6031

%N 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.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

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

%Y Cf. A001222, A303110.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Apr 18 2018