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A139141
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For n>=1, a(n) = floor[(d(p(n)+1) + d(p(n)+2) + d(p(n)+3) +...+d(p(n+1)))/(p(n+1)-p(n))], where d(m) is the number of positive divisors of m and p(n) is the n-th prime. a(0) = floor[(d(1) + d(2))/2].
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2
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1, 2, 2, 3, 3, 4, 3, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 7, 5, 5, 7, 5, 5, 5, 6, 5, 5, 5, 7, 6, 5, 5, 6, 5, 6, 7, 6, 6, 5, 6, 5, 10, 6, 8, 5, 7, 6, 6, 6, 7, 6, 6, 11, 5, 7, 6, 6, 9, 7, 7, 5, 6, 7, 6, 9, 6, 7, 7, 6, 7, 8, 5, 7, 7, 7, 5, 7, 8, 7, 7, 6, 13, 6, 11, 6, 8, 6, 7, 6, 9, 6, 7, 8, 6, 7, 5, 8, 7, 7, 7, 7, 6, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The sequence approximates the average number of divisors over all integers between consecutive primes.
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FORMULA
| For n>= 1, a(n) = floor[A139140(n)/A001223(n)].
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EXAMPLE
| The 9th prime is 23 and the 10th prime is 29. So a(9) = floor[d(24) + d(25) + d(26) + d(27) + d(28) + d(29))/6] = floor[(8 + 3 + 4 + 4 + 6 + 2)/6] = floor[27/6] = 4.
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MAPLE
| A139141 := proc(n) if n = 0 then 1; else add(numtheory[tau](k), k=ithprime(n)+1..ithprime(n+1)) ; floor(%/(ithprime(n+1)-ithprime(n))) ; fi; end proc: seq(A139141(n), n=0..120) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009]
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CROSSREFS
| Cf. A139140.
Sequence in context: A196048 A176075 A117119 * A122953 A128998 A137813
Adjacent sequences: A139138 A139139 A139140 * A139142 A139143 A139144
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Apr 10 2008
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EXTENSIONS
| Extended beyond a(11) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009
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