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A281086 Denominator of sum of reciprocals of numbers less than n that do not divide n. 1
1, 1, 2, 3, 12, 20, 20, 70, 840, 504, 2520, 27720, 27720, 51480, 360360, 180180, 720720, 1361360, 4084080, 77597520, 15519504, 470288, 5173168, 356948592, 1784742960, 686439600, 26771144400, 80313433200, 80313433200, 2329089562800, 2329089562800, 36100888223400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..32.

FORMULA

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

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

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

EXAMPLE

a(6) = 20 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[Denominator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]

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

CROSSREFS

Cf. A000203, A001008, A002805, A017665, A017666, A024816, A277791, A281085 (numerators).

Sequence in context: A056700 A299547 A140989 * A130089 A323119 A307035

Adjacent sequences:  A281083 A281084 A281085 * A281087 A281088 A281089

KEYWORD

nonn,frac

AUTHOR

Ilya Gutkovskiy, Jan 14 2017

STATUS

approved

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Last modified April 25 12:19 EDT 2019. Contains 322456 sequences. (Running on oeis4.)