A302642 Number of partitions of n into two parts such that the positive difference of the parts is semiprime.

0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 1, 3, 1, 4, 2, 4, 2, 4, 2, 4, 3, 5, 3, 5, 4, 6, 4, 6, 4, 6, 4, 6, 5, 7, 6, 7, 6, 8, 7, 8, 7, 8, 7, 8, 7, 9, 7, 9, 8, 9, 9, 9, 9, 9, 10, 9, 11, 10, 11, 10, 11, 11, 11, 11, 12, 11, 12, 11, 13, 11, 13, 11, 13, 12, 13, 12, 14

Offset

1,8

Links

Table of n, a(n) for n=1..79.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[KroneckerDelta[PrimeOmega[n - 2 i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]

Prog

(PARI) a(n) = sum(i=1, (n-1)\2, bigomega(n-2*i)==2); \\ Michel Marcus, Apr 11 2018

Crossrefs

Cf. A001222, A302604, A302643.

Sequence in context: A306696 A237184 A029240 * A025803 A029185 A029184

Adjacent sequences: A302639 A302640 A302641 * A302643 A302644 A302645

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 10 2018

Status

approved