A281085 Numerator of sum of reciprocals of numbers less than n that do not divide n.

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

Offset: 1

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn
• frac

Examples

			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, ...
		

Crossrefs

Cf. A000203, A001008, A002805, A017665, A017666, A024816, A277790, A281086 (denominators).

Programs

Mathematica

Table[Numerator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]
Table[Numerator[HarmonicNumber[n] - DivisorSigma[1, n]/n], {n, 1, 32}]

Formula

a(n) = numerator(H_n - Sum_{d|n} 1/d), where H_n is the n-th harmonic number.

a(n) = numerator(A001008(n)/A002805(n) - A000203(n)/n).

Numerators of coefficients in expansion of -log(1 - x)/(1 - x) - Sum_{k>=1} log(1/(1 - x^k)).