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A057020
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Numerator of (sum of divisors of n / number of divisors of n).
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14
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1, 3, 2, 7, 3, 3, 4, 15, 13, 9, 6, 14, 7, 6, 6, 31, 9, 13, 10, 7, 8, 9, 12, 15, 31, 21, 10, 28, 15, 9, 16, 21, 12, 27, 12, 91, 19, 15, 14, 45, 21, 12, 22, 14, 13, 18, 24, 62, 19, 31, 18, 49, 27, 15, 18, 15, 20, 45, 30, 14, 31, 24, 52, 127, 21, 18, 34, 21, 24, 18
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OFFSET
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1,2
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COMMENTS
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Numerator of arithmetic mean of the divisors of n. - Jaroslav Krizek, Apr 26 2010
The average order of a(n)/A057021(n) is asymptotic to n/sqrt(log(n)); see the Bateman et al. link or the Sutantyo link. - Charles R Greathouse IV, May 17 2012
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LINKS
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FORMULA
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EXAMPLE
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a(12) = 14 since the 6 factors of 12 are 1, 2, 3, 4, 6 and 12 and 1 + 2 + 3 + 4 + 6 + 12 = 28 and 28/6 = 14/3.
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MAPLE
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with(numtheory): seq(numer(sigma(n)/tau(n)), n=1..70) ; # Zerinvary Lajos, Jun 04 2008
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MATHEMATICA
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Numerator[Table[(Plus @@ Divisors[n])/Length[Divisors[n]], {n, 70}]] (* Alonso del Arte, Feb 24 2006 *)
Table[Numerator[DivisorSigma[1, n]/DivisorSigma[0, n]], {n, 100}] (* Harvey P. Dale, Dec 19 2023 *)
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PROG
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(Haskell)
import Data.Ratio ((%), numerator)
a057020 n = numerator $ a000203 n % a000005 n
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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