A281086 Denominator of sum of reciprocals of numbers less than n that do not divide n.

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

Offset: 1

Author

Ilya Gutkovskiy, Jan 14 2017

Keywords

• nonn
• frac

Examples

			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, ...
		

Crossrefs

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

Programs

Mathematica

Table[Denominator[HarmonicNumber[n] - DivisorSigma[-1, n]], {n, 1, 32}]
Table[Denominator[HarmonicNumber[n] - DivisorSigma[1, n]/n], {n, 1, 32}]
Table[Denominator[Total[1/Complement[Range[n],Divisors[n]]]],{n,40}] (* Harvey P. Dale, Jan 04 2020 *)

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)).