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A199331
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Number of ordered ways of writing n as the sum of two semiprimes.
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3
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0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 0, 3, 4, 3, 2, 0, 2, 4, 4, 2, 2, 3, 4, 5, 6, 4, 0, 2, 6, 6, 4, 2, 6, 6, 4, 5, 8, 7, 4, 2, 8, 10, 6, 5, 2, 5, 6, 4, 10, 6, 4, 4, 10, 12, 12, 2, 6, 10, 6, 7, 8, 9, 6, 5, 12, 14, 10, 6, 6, 7, 8, 7, 10, 10, 6, 4, 14, 14
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OFFSET
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1,10
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COMMENTS
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Conjecture: Only the integers 1, 2, 3, 4, 5, 6, 7, 9, 11, 17, 22, 33 (A072966) cannot be partitioned into a set of two semiprimes.
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LINKS
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FORMULA
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MAPLE
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sp:= select(t -> numtheory:-bigomega(t)=2, [$1..100]):
G:= expand(add(x^t, t=sp)^2):
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MATHEMATICA
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mx=200; semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; t = Select[ Range@ mx, semiPrimeQ]; s = Sort[Plus @@@ Tuples[t, 2]]; Transpose[ Tally@ Join[ Range@ mx, s]][[2]] - 1
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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