|
|
A110566
|
|
a(n) = lcm{1,2,...,n}/denominator of harmonic number H(n).
|
|
24
|
|
|
1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 15, 45, 45, 45, 15, 3, 3, 1, 1, 1, 1, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 77, 77, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 27, 27, 27, 9, 9, 9, 3, 3, 3, 3, 3, 33, 33, 33, 33, 11, 11, 11, 11, 11, 11, 11, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
a(n) is always odd.
Unsorted union: 1, 3, 15, 45, 11, 77, 7, 9, 27, 33, 25, 5, 55, 275, 13, 39, 17, 49, 931, 19, 319, 75, ..., . See A112810.
It is conjectured that every odd number occurs in this sequence (see A112822 for the first occurrence of each of them). - Jianing Song, Nov 28 2022
|
|
LINKS
|
|
|
FORMULA
|
a(n) = gcd(lcm{1,2,...,n}, H(n)*lcm{1,2,...,n}).
|
|
EXAMPLE
|
a(6) = 60/20 = 3 because lcm{1,2,3,4,5,6}=60 and H(6)=49/20.
|
|
MAPLE
|
H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
L:= proc(n) L(n):= ilcm(n, `if`(n=1, 1, L(n-1))) end:
a:= n-> L(n)/denom(H(n)):
|
|
MATHEMATICA
|
f[n_] := LCM @@ Range[n]/Denominator[HarmonicNumber[n]]; Table[ f[n], {n, 90}] (* Robert G. Wilson v, Sep 15 2005 *)
|
|
PROG
|
(PARI) a(n) = lcm(vector(n, k, k))/denominator(sum(k=1, n, 1/k)); \\ Michel Marcus, Mar 07 2018
(Python)
from sympy import lcm, harmonic
def A110566(n): return lcm([k for k in range(1, n+1)])//harmonic(n).q # Chai Wah Wu, Mar 06 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|