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A111880 Denominators of array which counts positive rational numbers (not including natural numbers). 3
2, 3, 4, 3, 2, 5, 6, 5, 4, 3, 2, 7, 5, 3, 8, 7, 5, 4, 2, 9, 7, 3, 10, 9, 8, 7, 6, 5, 4, 3, 2, 11, 7, 5, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 13, 11, 9, 5, 3, 14, 13, 11, 8, 7, 4, 2, 15, 13, 11, 9, 7, 5, 3, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 17, 13, 11, 7, 5, 18, 17, 16, 15, 14, 13, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Numerators are given by A111879.

The method to obtain the rationals r(n,k) for row n is described under A111879.

REFERENCES

P. Dienes, The Taylor Series, Dover 1957, p. 8, eq.(1).

LINKS

Table of n, a(n) for n=3..93.

W. Lang, Array of ratios and more.

FORMULA

a(n, k)=denominator(r(n, k)), n>=3, k=1..phi(n)-1, with phi(n):=A000010(n) (Euler's totient function) and the ratios r(n, k) are defined for row n in A111879.

EXAMPLE

[2], [3], [4, 3, 2], [5], [6, 5, 4, 3, 2], [7, 5, 3], [8, 7, 5, 4,

2], [9, 7, 3],...

The corresponding rationals are: [1/2], [1/3], [1/4, 2/3, 3/2],

[1/5], [1/6, 2/5, 3/4, 4/3, 5/2], [1/7, 3/5, 5/3], [1/8, 2/7, 4/5, 5/4, 7/2],

[1/9, 3/7, 7/3],...

CROSSREFS

Cf. A020652/A020653 if natural numbers are included.

Sequence in context: A341861 A303597 A251102 * A306461 A101497 A274007

Adjacent sequences:  A111877 A111878 A111879 * A111881 A111882 A111883

KEYWORD

nonn,easy,frac,tabf

AUTHOR

Wolfdieter Lang, Aug 23 2005

STATUS

approved

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)