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A105149
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Number of even semiprimes k such that n^2 < k <= (n+1)^2.
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2
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0, 1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 3, 3, 2, 4, 2, 3, 3, 4, 5, 1, 6, 3, 5, 3, 4, 4, 5, 4, 6, 5, 5, 3, 6, 5, 7, 6, 4, 6, 5, 7, 6, 5, 6, 6, 8, 8, 5, 6, 8, 7, 6, 5, 9, 9, 7, 10, 6, 7, 8, 5, 10, 6, 10, 9, 8, 8, 10, 8, 11, 5, 9, 9, 13, 10, 9, 9, 9, 8, 8, 10, 12, 7, 11, 12, 12, 10, 10, 12, 10, 12, 10, 10, 10, 11
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OFFSET
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0,4
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COMMENTS
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a(n)>=1 because there is always a number 2*prime(i) between n^2 and (n+1)^2 for n>0.
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LINKS
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EXAMPLE
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a(6)=2 because between 5^2 and 6^2 there are two 2*prime(i): 2*prime(6)=2*13 and 2*prime(7)=2*17.
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MAPLE
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L:= map(numtheory:-pi, [seq(floor(n^2/2), n=0..100)]):
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MATHEMATICA
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f[n_] := PrimePi[Floor[n^2/2]]; Table[f[(n + 1)] - f[n], {n, 0, 100}]
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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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