OFFSET
2,3
COMMENTS
Denominators are given in A323185.
From its prime factorization, each natural number N>1 can be uniquely represented as a tuple of nondecreasing first powers (e.g., 60 = 2*2*3*5 -> (2, 2, 3, 5)).
There is a unique positive finite continued fraction associated with N whose coefficients in the standard abbreviated notation (except for the first coefficient, which is arbitrarily set to zero) map 1-to-1 to the elements of the tuple, from which the corresponding generating rational can be calculated (e.g. 60 -> [0; 2, 2, 3, 5] = 37/90).
The first few generating rationals are:
N ... GR .... continued fraction
2 ... 1/2 ... [0; 2]
3 ... 1/3 ... [0; 3]
4 ... 2/5 ... [0; 2, 2]
5 ... 1/5 ... [0; 5]
6 ... 3/7 ... [0; 2, 3]
7 ... 1/7 ... [0; 7]
8 ... 5/12 .. [0; 2, 2, 2]
9 ... 3/10 .. [0; 3, 3]
10 .. 5/11 .. [0; 2, 5]
a(n) is the numerator of the generating rational of n.
Iff n is prime, a(n) is 1.
LINKS
Georg Fischer, Table of n, a(n) for n = 2..1000
EXAMPLE
a(28) = 15 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.
a(29) = 1 because 1/29 = [0; 29] = 29.
MATHEMATICA
Array[Numerator@ FromContinuedFraction@ Prepend[Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #], 0] &, 74, 2] (* Michael De Vlieger, Jan 07 2019 *)
PROG
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Chris Boyd, Jan 06 2019
STATUS
approved