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A303113
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Number of partitions of n into two distinct positive integers (s,t), s < t, such that t is semiprime and |t-s| is not semiprime.
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0
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0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 2, 1, 2, 0, 3, 2, 4, 2, 2, 1, 1, 2, 3, 2, 4, 4, 4, 3, 3, 2, 3, 3, 3, 4, 3, 4, 5, 4, 8, 5, 6, 5, 4, 3, 4, 4, 7, 6, 7, 7, 6, 5, 4, 5, 6, 5, 6, 8, 5, 8, 7, 8, 8, 6, 9, 8, 7, 7, 8, 8, 9, 6, 7, 10, 8, 6, 6, 8, 8, 7, 6, 9, 7, 9, 9, 10
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OFFSET
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1,7
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor((n-1)/2)} [Omega(n-i) = 2] * (1-[Omega(n-2*i) = 2]), where [] is the Iverson bracket and Omega = A001222.
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MATHEMATICA
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Table[Sum[KroneckerDelta[PrimeOmega[n - i], 2] (1 - KroneckerDelta[PrimeOmega[n - 2 i], 2]), {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Count[IntegerPartitions[n, {2}], _?(PrimeOmega[#[[1]]]==2 && PrimeOmega[ #[[1]]-#[[2]]]!=2&)], {n, 100}] (* Harvey P. Dale, Jun 30 2021 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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