A303119 - OEIS

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A303119

Number of partitions of n into two parts (p,q) with p <= q such that p is semiprime and q is squarefree.

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

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OFFSET

1,17

LINKS

Table of n, a(n) for n=1..85.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor(n/2)} mu(n-i)^2 * [Omega(i) = 2], where [] is the Iverson bracket, mu = A008683 and Omega = A001222.

MATHEMATICA

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

CROSSREFS

Cf. A001222, A008683, A302538.