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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Consider the array T(r,c) where is the number of r-almost primes less than or equal to r^c, starting with a(0)=1. This is the diagonal just above the main diagonal.
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EXAMPLE
| a(3)=5 because there are five 3-almost primes <= 27, 8,12,18,20&27.
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MATHEMATICA
| 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 Weisstein (eww(AT)wolfram.com) Feb 07 2006
Do[ Print@ AlmostPrimePi[n, n^n], {n, 13}]
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CROSSREFS
| Cf. A116433, A116434.
Sequence in context: A002776 A081342 A058248 * A090367 A189488 A111557
Adjacent sequences: A116432 A116433 A116434 * A116436 A116437 A116438
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KEYWORD
| hard,more,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 15 2006
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EXTENSIONS
| a(13)-a(14) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 05 2010
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