|
|
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
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy,frac,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|