A375517 a(n) = A375516(n)/n.

2, 2, 4, 12, 240, 40200, 1385211600, 1469089808430082650, 1705264091048404496800363077779646800, 2355419752377504356995163180927294204575594409432081035253034399529376520

Offset: 1

Author

N. J. A. Sloane, Aug 20 2024

Keywords

• nonn

Examples

			The prime factors (without repetition) of the first ten terms are:
  {2},
  {2},
  {2},
  {2, 3},
  {2, 3, 5},
  {2, 3, 5, 67},
  {2, 3, 5, 67, 5743},
  {2, 3, 5, 7, 67, 5743, 1212060151},
  {2, 5, 7, 67, 137, 151, 5743, 10867, 1212060151, 5808829669},
  {2, 3, 5, 7, 19, 47, 67, 71, 137, 151, 5743, 10867, 1212060151, 5808829669, 243254025696427, 99509446928973841}
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A374663, A374983, A375516.

Programs

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))/n:
seq(a(n), n=1..10);  # Alois P. Heinz, Oct 19 2024

Mathematica

s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(n*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*n)];
a[n_] := Denominator[s[n]]/n;
Table[a[n], {n, 1, 10}] (* Jean-François Alcover, Mar 21 2025, after Alois P. Heinz *)

Python

from itertools import count, islice
from math import gcd
def A375517_gen(): # generator of terms
    p, q = 0, 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
        yield q//k
A375517_list = list(islice(A375517_gen(),11)) # Chai Wah Wu, Aug 28 2024