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A224712
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The number of unordered partitions {a, b} of n such that a or b is composite and the other is prime.
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5
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0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 4, 2, 3, 2, 4, 2, 6, 2, 5, 3, 6, 3, 8, 2, 7, 4, 9, 5, 9, 3, 8, 6, 9, 4, 11, 3, 11, 8, 10, 6, 12, 4, 11, 7, 12, 7, 14, 4, 13, 7, 15, 9, 15, 5, 14, 10, 16, 9, 16, 4, 15, 12, 16, 8, 18, 6, 18, 14, 17, 9, 19, 7, 18, 11, 19, 11, 21
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OFFSET
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1,9
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LINKS
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EXAMPLE
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For n = 6, in the set {{5, 1}, {4, 2}, {3, 3}}, {4, 2} is the only partition that satisfies the requirements, so a(6) = 1.
For n = 9, we have partitions {6, 3} and {5, 4}, so a(9) = 2.
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MATHEMATICA
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Table[Length[Select[Range[2, Floor[n/2]], (PrimeQ[#] && Not[PrimeQ[n - #]]) || (Not[PrimeQ[#]] && PrimeQ[n - #]) &]], {n, 80}] (* Alonso del Arte, Apr 21 2013 *)
Table[Count[IntegerPartitions[n, {2}], _?(FreeQ[#, 1]&&Total[Boole[ PrimeQ[ #]]] == 1&)], {n, 80}] (* Harvey P. Dale, Jul 21 2021 *)
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PROG
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CROSSREFS
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Cf. A062602 (allows 1 as well as composites), A224708 (a and b are both composite).
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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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