login
A375520
a(n) = A375516(n)/LCM{1,...,n}.
1
1, 2, 2, 2, 4, 20, 4020, 23086860, 13991331508857930, 6090228896601444631429868134927310, 9346903779275810940456996749711484938792041307270162838305692061624510
OFFSET
0,2
COMMENTS
It is a theorem of Rémy Sigrist (see the proof in A374983) that a(n) is an integer.
LINKS
MAPLE
s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
a:= n-> denom(s(n))/ilcm($1..n):
seq(a(n), n=0..10); # Alois P. Heinz, Oct 19 2024
PROG
(Python)
from itertools import count, islice
from math import gcd, lcm
def A375520_gen(): # generator of terms
p, q, c = 0, 1, 1
for k in count(1):
m = q//(k*(q-p))+1
p, q = p*k*m+q, k*m*q
p //= (r:=gcd(p, q))
q //= r
c = lcm(c, k)
yield q//c
A375520_list = list(islice(A375520_gen(), 11)) # Chai Wah Wu, Aug 28 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 28 2024
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 19 2024
STATUS
approved