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 A057020 Numerator of (sum of divisors of n / number of divisors of n). 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 V. Arnold, Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics, Journal of Mathem. Fluid Mechanics 7 (2005), pp. S4-S50. Paul T. Bateman, Paul Erdős, Carl Pomerance, and Ernst G. Straus, The arithmetic mean of the divisors of an integer in Analytic Number Theory (1980), pp. 197-220. Daniel Sutantyo, Elementary and Analytic Methods in Number Theory, M.S. thesis (Macquarie University, 2007), chapter 3. FORMULA a(n) = A057021(n) * A000203(n)/A000005(n) = A000203(n)/A009205(n) = (A057022(n) + A054025(n)/A000005(n)) * A057021(n). EXAMPLE 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. MAPLE with(numtheory): seq(numer(sigma(n)/tau(n)), n=1..70) ; # Zerinvary Lajos, Jun 04 2008 MATHEMATICA Numerator[Table[(Plus @@ Divisors[n])/Length[Divisors[n]], {n, 70}]] (* Alonso del Arte, Feb 24 2006 *) PROG (Haskell) import Data.Ratio ((%), numerator) a057020 n = numerator \$ a000203 n % a000005 n -- Reinhard Zumkeller, Jan 06 2012 (PARI) a(n)=numerator(sigma(n)/numdiv(n)) \\ Charles R Greathouse IV, May 17 2012 CROSSREFS Cf. A000005, A000203, A009205, A054025, A057021 (denominator), A057022. Sequence in context: A182891 A071190 A295314 * A257322 A276466 A289336 Adjacent sequences:  A057017 A057018 A057019 * A057021 A057022 A057023 KEYWORD frac,nonn AUTHOR Henry Bottomley, Jul 21 2000 STATUS approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)