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A116435
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Number of n-almost primes less than or equal to n^n.
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1
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0, 1, 5, 34, 269, 2613, 28893, 359110, 4934952, 74342563, 1217389949, 21533211312, 409230368646, 8318041706593
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OFFSET
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1,3
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COMMENTS
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Consider the array T(r,c) where is the number of c-almost primes less than or equal to r^c. This is the diagonal T(r,r).
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LINKS
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EXAMPLE
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a(3)=5 because there are five 3-almost primes <= 27, 8,12,18,20&27.
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MATHEMATICA
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AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]] ]]]; Eric W. Weisstein Feb 07 2006
Do[ Print@ AlmostPrimePi[n, n^n], {n, 13}]
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CROSSREFS
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KEYWORD
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hard,more,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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