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a(n) = A375516(n)/n.
5

%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