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A281085
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Numerator of sum of reciprocals of numbers less than n that do not divide n.
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1
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0, 0, 1, 1, 13, 9, 29, 59, 1163, 569, 4861, 21341, 58301, 79139, 619181, 260041, 1715839, 1808487, 10190221, 116220883, 32925391, 966183, 13920029, 455451475, 4597423223, 1536962359, 64517796001, 154777722503, 235091155703, 3714867879427, 6975593267347, 75441657715841
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = numerator(H_n - Sum_{d|n} 1/d), where H_n is the n-th harmonic number.
Numerators 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) = 9 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[Numerator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]
Table[Numerator[HarmonicNumber[n] - DivisorSigma[1, n]/n], {n, 1, 32}]
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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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