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

%I A375517 #22 Mar 21 2025 10:32:45
%S A375517 2,2,4,12,240,40200,1385211600,1469089808430082650,
%T A375517 1705264091048404496800363077779646800,
%U A375517 2355419752377504356995163180927294204575594409432081035253034399529376520
%N A375517 a(n) = A375516(n)/n.
%H A375517 Alois P. Heinz, <a href="/A375517/b375517.txt">Table of n, a(n) for n = 1..14</a>
%e A375517 The prime factors (without repetition) of the first ten terms are:
%e A375517   {2},
%e A375517   {2},
%e A375517   {2},
%e A375517   {2, 3},
%e A375517   {2, 3, 5},
%e A375517   {2, 3, 5, 67},
%e A375517   {2, 3, 5, 67, 5743},
%e A375517   {2, 3, 5, 7, 67, 5743, 1212060151},
%e A375517   {2, 5, 7, 67, 137, 151, 5743, 10867, 1212060151, 5808829669},
%e A375517   {2, 3, 5, 7, 19, 47, 67, 71, 137, 151, 5743, 10867, 1212060151, 5808829669, 243254025696427, 99509446928973841}
%p A375517 s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
%p A375517 b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
%p A375517 a:= n-> denom(s(n))/n:
%p A375517 seq(a(n), n=1..10);  # _Alois P. Heinz_, Oct 19 2024
%t A375517 s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(n*b[n])];
%t A375517 b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*n)];
%t A375517 a[n_] := Denominator[s[n]]/n;
%t A375517 Table[a[n], {n, 1, 10}] (* _Jean-François Alcover_, Mar 21 2025, after _Alois P. Heinz_ *)
%o A375517 (Python)
%o A375517 from itertools import count, islice
%o A375517 from math import gcd
%o A375517 def A375517_gen(): # generator of terms
%o A375517     p, q = 0, 1
%o A375517     for k in count(1):
%o A375517         m = q//(k*(q-p))+1
%o A375517         p, q = p*k*m+q, k*m*q
%o A375517         p //= (r:=gcd(p,q))
%o A375517         q //= r
%o A375517         yield q//k
%o A375517 A375517_list = list(islice(A375517_gen(),11)) # _Chai Wah Wu_, Aug 28 2024
%Y A375517 Cf. A374663, A374983, A375516.
%K A375517 nonn
%O A375517 1,1
%A A375517 _N. J. A. Sloane_, Aug 20 2024