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A295630
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Number of partitions of n into two distinct parts that are not both prime.
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0
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0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 5, 5, 6, 5, 8, 6, 8, 7, 9, 8, 11, 8, 11, 10, 13, 11, 14, 11, 14, 13, 15, 13, 17, 13, 18, 17, 18, 16, 20, 16, 20, 18, 21, 19, 23, 18, 23, 20, 25, 22, 26, 21, 26, 24, 28, 25, 29, 23, 29, 28, 30, 26, 32, 26, 33, 31, 33, 29
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OFFSET
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1,6
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LINKS
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FORMULA
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EXAMPLE
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a(12) = 4; The partitions of 12 into two distinct parts are (11,1), (10,2), (9,3), (8,4) and (7,5). Of these partitions, the parts in (11,1), (10,2), (9,3) and (8,4) are not both prime, so a(12) = 4.
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MATHEMATICA
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Table[Sum[1 - (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}]
Table[Count[IntegerPartitions[n, {2}], _?(#[[1]]!=#[[2]]&&Total[Boole[ PrimeQ[ #]]]<2&)], {n, 70}] (* Harvey P. Dale, May 18 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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