%I #19 Oct 19 2024 20:45:42
%S 2,2,4,12,240,40200,1385211600,1469089808430082650,
%T 1705264091048404496800363077779646800,
%U 2355419752377504356995163180927294204575594409432081035253034399529376520
%N a(n) = A375516(n)/n.
%H Alois P. Heinz, <a href="/A375517/b375517.txt">Table of n, a(n) for n = 1..14</a>
%e The prime factors (without repetition) of the first ten terms are:
%e {2},
%e {2},
%e {2},
%e {2, 3},
%e {2, 3, 5},
%e {2, 3, 5, 67},
%e {2, 3, 5, 67, 5743},
%e {2, 3, 5, 7, 67, 5743, 1212060151},
%e {2, 5, 7, 67, 137, 151, 5743, 10867, 1212060151, 5808829669},
%e {2, 3, 5, 7, 19, 47, 67, 71, 137, 151, 5743, 10867, 1212060151, 5808829669, 243254025696427, 99509446928973841}
%p s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
%p b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
%p a:= n-> denom(s(n))/n:
%p seq(a(n), n=1..10); # _Alois P. Heinz_, Oct 19 2024
%o (Python)
%o from itertools import count, islice
%o from math import gcd
%o def A375517_gen(): # generator of terms
%o p, q = 0, 1
%o for k in count(1):
%o m = q//(k*(q-p))+1
%o p, q = p*k*m+q, k*m*q
%o p //= (r:=gcd(p,q))
%o q //= r
%o yield q//k
%o A375517_list = list(islice(A375517_gen(),11)) # _Chai Wah Wu_, Aug 28 2024
%Y Cf. A374663, A374983, A375516.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 20 2024