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A096509
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Number of prime-powers [including primes] in the (up and down) neighborhood of n with Ceiling[Log[n]] radius.
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26
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0, 2, 4, 4, 4, 4, 4, 5, 4, 5, 4, 3, 3, 4, 3, 4, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 5, 5, 5, 4, 4, 3, 4, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 3, 4, 4, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 4, 3, 4, 4
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OFFSET
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1,2
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COMMENTS
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With increasing n the radius of log(n) slowly increases, while frequency of prime-powers decreases. Thus hard to estimate upper bound of terms in this sequence.
Heuristically a(n) = 0 about 1/e^2 = 13.53...% of the time. The first few instances are 1, 300, 324, 895, 896, 897, 898, 899, 1077, .... - Charles R Greathouse IV, Apr 30 2015
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LINKS
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FORMULA
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EXAMPLE
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n=284736: in [284723,284749] around n, 8 prime(powers) occur,radius=13, a[284736]=8.
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MATHEMATICA
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a[n_] := Select[Range[n - Ceiling[Log[n]], n + Ceiling[Log[n]]], PrimePowerQ] // Length; Array[a, 105] (* Jean-François Alcover, Oct 06 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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