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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.
1
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
OFFSET
1,17
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 18 2018
STATUS
approved