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Search: id:A120041
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| A120041 |
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Number of 10-almost primes 10ap such that 2^n < 10ap <= 2^(n+1). |
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+0
30
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 47, 103, 233, 487, 1072, 2246, 4803, 10202, 21440, 45115, 94434, 197891, 412010, 858846, 1783610, 3700698, 7665755, 15853990, 32750248, 67564405, 139238488, 286625278, 589472979, 1211146741, 2486322304
(list; graph; listen)
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OFFSET
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0,12
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COMMENT
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The partial sum equals the number of Pi_10(2^n).
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EXAMPLE
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(2^10, 2^11] there is one semiprime, namely 1536. 1024 was counted in the previous entry.
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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 (eww(AT)wolfram.com) Feb 07 2006 *)
t = Table[AlmostPrimePi[10, 2^n], {n, 0, 39}]; Rest@t - Most@t
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CROSSREFS
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Cf. A046314, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.
Sequence in context: A120038 A120039 A120040 this_sequence A120042 A120043 A063897
Adjacent sequences: A120038 A120039 A120040 this_sequence A120042 A120043 A120044
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 21 2006
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