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Search: id:A116435
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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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+0
2
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| 0, 1, 5, 34, 269, 2613, 28893, 359110, 4934952, 74342563, 1217389949, 21533211312
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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
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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 Weisstein (eww(AT)wolfram.com) Feb 07 2006
Do[ Print@ AlmostPrimePi[n, n^n], {n, 13}]
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CROSSREFS
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Cf. A116433, A116434.
Sequence in context: A002776 A081342 A058248 this_sequence A090367 A111557 A121323
Adjacent sequences: A116432 A116433 A116434 this_sequence A116436 A116437 A116438
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KEYWORD
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hard,more,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 15 2006
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