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%I #7 Jan 15 2017 11:45:41
%S 0,0,1,1,13,9,29,59,1163,569,4861,21341,58301,79139,619181,260041,
%T 1715839,1808487,10190221,116220883,32925391,966183,13920029,
%U 455451475,4597423223,1536962359,64517796001,154777722503,235091155703,3714867879427,6975593267347,75441657715841
%N Numerator of sum of reciprocals of numbers less than n that do not divide n.
%F a(n) = numerator(H_n - Sum_{d|n} 1/d), where H_n is the n-th harmonic number.
%F a(n) = numerator(A001008(n)/A002805(n) - A000203(n)/n).
%F Numerators of coefficients in expansion of -log(1 - x)/(1 - x) - Sum_{k>=1} log(1/(1 - x^k)).
%e 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.
%e 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, ...
%t Table[Numerator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]
%t Table[Numerator[HarmonicNumber[n] - DivisorSigma[1, n]/n], {n, 1, 32}]
%Y Cf. A000203, A001008, A002805, A017665, A017666, A024816, A277790, A281086 (denominators).
%K nonn,frac
%O 1,5
%A _Ilya Gutkovskiy_, Jan 14 2017