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A059247
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Denominator of Sum_{j=1..n} d(j)/n, where d = number of divisors function (A000005).
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3
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1, 2, 3, 1, 1, 3, 7, 2, 9, 10, 11, 12, 13, 14, 1, 8, 17, 9, 19, 10, 3, 11, 23, 2, 25, 2, 27, 28, 29, 10, 31, 32, 11, 34, 35, 9, 37, 19, 13, 20, 41, 1, 43, 1, 45, 23, 1, 8, 49, 50, 51, 52, 53, 54, 5, 56, 19, 58, 59, 20, 61, 62, 3, 8, 65, 33, 67, 17, 69, 35, 71
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OFFSET
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1,2
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REFERENCES
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M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 1999; see p. 135.
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LINKS
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FORMULA
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EXAMPLE
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1, 3/2, 5/3, 2, 2, 7/3, 16/7, 5/2, 23/9, 27/10, ...
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MATHEMATICA
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Denominator[Table[Sum[DivisorSigma[0, j]/n, {j, 1, n}], {n, 1, 100}]] (* G. C. Greubel, Jan 02 2016 *)
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PROG
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(PARI) a(n) = denominator(sum(j=1, n, numdiv(j))/n); \\ Michel Marcus, Jan 03 2017
(Python)
from math import isqrt, gcd
def A059247(n): return n//gcd(n, (lambda m: 2*sum(n//k for k in range(1, m+1))-m*m)(isqrt(n))) # Chai Wah Wu, Oct 08 2021
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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