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A281085 Numerator of sum of reciprocals of numbers less than n that do not divide n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)