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

1,5

Links

Table of n, a(n) for 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)).

Example

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, ...

Mathematica

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

Crossrefs

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

Sequence in context: A305043 A066552 A206609 * A072270 A214025 A240812

Adjacent sequences: A281082 A281083 A281084 * A281086 A281087 A281088

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Jan 14 2017

Status

approved