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A111879 Numerators of array which counts positive rational numbers (not including natural numbers). 4
1, 1, 1, 2, 3, 1, 1, 2, 3, 4, 5, 1, 3, 5, 1, 2, 4, 5, 7, 1, 3, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 5, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 3, 5, 9, 11, 1, 2, 4, 7, 8, 11, 13, 1, 3, 5, 7, 9, 11, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 5, 7, 11, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

COMMENTS

Denominators are given by A111880.

The sequence of row lengths is [1, 1, 3, 1, 5, 3, 5, 3, 9, 3, 11, 5, 7, 7, ...] = A000010(n)-1 = phi(n)-1, with Euler's totient function phi(n).

For n>=3 delete from the list [seq(j/n-j,j=1..n-2)] the natural numbers and the ratios p/q with (p,q) not 1 (p and q not relatively prime, i.e., p and q have a common divisor >1).

REFERENCES

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

LINKS

Table of n, a(n) for n=3..98.

W. Lang, Array of ratios and more.

FORMULA

a(n, k)=numerator(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) defined for row n above.

EXAMPLE

[1], [1], [1, 2, 3], [1], [1, 2, 3, 4, 5], [1, 3, 5], [1, 2, 4, 5,

7], [1, 3, 7],...

The corresponding ratios 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

Row sums give A111881(n)/A069220(n), n>=3, see the W. Lang link.

Cf. A020652/A020653 if natural numbers are included.

Sequence in context: A330957 A327192 A157813 * A193280 A114732 A123338

Adjacent sequences:  A111876 A111877 A111878 * A111880 A111881 A111882

KEYWORD

nonn,easy,frac,tabf

AUTHOR

Wolfdieter Lang, Aug 23 2005

STATUS

approved

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Last modified September 22 13:15 EDT 2021. Contains 347607 sequences. (Running on oeis4.)