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A281086
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Denominator of sum of reciprocals of numbers less than n that do not divide n.
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2
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1, 1, 2, 3, 12, 20, 20, 70, 840, 504, 2520, 27720, 27720, 51480, 360360, 180180, 720720, 1361360, 4084080, 77597520, 15519504, 470288, 5173168, 356948592, 1784742960, 686439600, 26771144400, 80313433200, 80313433200, 2329089562800, 2329089562800, 36100888223400
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = denominator(H_n - Sum_{d|n} 1/d), where H_n is the n-th harmonic number.
Denominators of coefficients in expansion of -log(1 - x)/(1 - x) - Sum_{k>=1} log(1/(1 - x^k)).
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EXAMPLE
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a(6) = 20 because 6 has 4 divisors {1,2,3,6} therefore 2 non-divisors {4,5} and 1/4 + 1/5 = 9/20.
0, 0, 1/2, 1/3, 13/12, 9/20, 29/20, 59/70, 1163/840, 569/504, 4861/2520, 21341/27720, 58301/27720, 79139/51480, 619181/360360, 260041/180180, ...
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MATHEMATICA
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Table[Denominator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]
Table[Denominator[HarmonicNumber[n] - DivisorSigma[1, n]/n], {n, 1, 32}]
Table[Denominator[Total[1/Complement[Range[n], Divisors[n]]]], {n, 40}] (* Harvey P. Dale, Jan 04 2020 *)
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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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