A303110 Number of partitions of n into two parts (p,q), with p < q, such that neither p+q nor |q-p| is semiprime.

0, 0, 1, 0, 2, 0, 3, 1, 0, 0, 4, 2, 5, 0, 0, 3, 6, 4, 7, 5, 0, 0, 8, 6, 0, 0, 9, 7, 10, 8, 11, 9, 0, 0, 0, 10, 12, 0, 0, 11, 13, 12, 14, 13, 15, 0, 16, 14, 0, 15, 0, 16, 17, 17, 0, 18, 0, 0, 18, 19, 19, 0, 20, 20, 0, 21, 21, 22, 0, 23, 22, 24, 23, 0, 24, 25

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[(1 - KroneckerDelta[PrimeOmega[n - 2 i], 2]) (1 - KroneckerDelta[PrimeOmega[n], 2]), {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Count[IntegerPartitions[n, {2}], _?(PrimeOmega[Total[#]]!=2&&PrimeOmega[ Abs[#[[1]]-#[[2]]]]!=2&)], {n, 80}] (* Harvey P. Dale, Jan 03 2019 *)

Crossrefs

Cf. A001222, A302642.

Sequence in context: A324379 A035165 A290256 * A079133 A143143 A158853

Adjacent sequences: A303107 A303108 A303109 * A303111 A303112 A303113

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 18 2018

Status

approved