A303336 Number of rectangles with semiprime area and dimensions p,q where n = p+q and p <= q.

0, 0, 0, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 3, 0, 2, 1, 2, 1, 4, 1, 3, 1, 4, 1, 2, 0, 3, 1, 2, 1, 5, 1, 5, 0, 2, 2, 4, 0, 4, 1, 3, 1, 4, 1, 5, 1, 5, 0, 4, 0, 5, 1, 4, 0, 5, 1, 6, 1, 3, 2, 5, 0, 7, 0, 2, 1, 6, 0, 6, 1, 5, 2, 5, 0, 8, 0, 4, 1, 5, 1, 8, 1, 6

Offset

1,5

Links

Table of n, a(n) for n=1..86.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[KroneckerDelta[PrimeOmega[i (n - i)], 2], {i, Floor[n/2]}], {n, 100}]

Prog

(PARI) a(n) = sum(i=1, n\2, bigomega(i*(n-i)) == 2); \\ Michel Marcus, Apr 22 2018

Crossrefs

Cf. A001222, A303115, A303337.

Sequence in context: A117166 A078996 A084610 * A361462 A129479 A261095

Adjacent sequences: A303333 A303334 A303335 * A303337 A303338 A303339

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 21 2018

Status

approved