A111880 Denominators of array which counts positive rational numbers (not including natural numbers).

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

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.

Wolfdieter 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

Triangle begins:
  [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.

Cf. A111879.

Sequence in context: A341861 A303597 A251102 * A348599 A306461 A101497

Adjacent sequences: A111877 A111878 A111879 * A111881 A111882 A111883

Keyword

nonn,easy,frac,tabf

Author

Wolfdieter Lang, Aug 23 2005

Status

approved