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A143143
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a(n) = the number of primes that exist between (but don't include) j and k, where j is the largest divisor of n that is <= sqrt(n) and k = the smallest divisor of n that is >= sqrt(n).
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3
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0, 0, 1, 0, 2, 0, 3, 1, 0, 1, 4, 0, 5, 2, 0, 0, 6, 1, 7, 0, 1, 3, 8, 1, 0, 4, 2, 1, 9, 0, 10, 2, 2, 5, 0, 0, 11, 6, 3, 1, 12, 0, 13, 2, 1, 7, 14, 1, 0, 1, 4, 3, 15, 1, 1, 0, 5, 8, 16, 1, 17, 9, 0, 0, 2, 1, 18, 4, 6, 0, 19, 0, 20, 10, 3, 5, 0, 2, 21, 0, 0, 11, 22, 1, 3, 12, 7, 0, 23, 0, 1, 6, 8, 13, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Owen Whitby, Table of n, a(n) for n=1..500
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EXAMPLE
| The divisors of 14 are 1,2,7,14. The two middle divisors are 2 and 7. Between 2 and 7 (and not including 2 and 7) there are 2 primes (3 and 5). So a(14) = 2.
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MATHEMATICA
| a143143[minn_, maxn_]:=Module[{d, ld, a, b, c, lst143143={}}, Do[d=Divisors[n ]; ld=Length[d]; If[OddQ[ld], AppendTo[lst143143, {n, 0}], a=ld/2; b=d[[a]]; c =d[[ a+1]]; AppendTo[lst143143, {n, PrimePi[c-1]-PrimePi[b]}]], {n, minn, maxn}]; Transpose[lst143143]//MatrixForm] - Owen Whitby (whitbyo(AT)acm.org), Oct 22 2008
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CROSSREFS
| Cf. A143144, A143145.
Sequence in context: A137448 A035165 A079133 * A158853 A190440 A054372
Adjacent sequences: A143140 A143141 A143142 * A143144 A143145 A143146
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Jul 27 2008
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EXTENSIONS
| a(16) to a(500) from Owen Whitby (whitbyo(AT)acm.org), Oct 22 2008
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