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%I #11 Aug 08 2021 19:48:02
%S 1,3,5,7,53,107,25,1501,563,901,12389,16519,322121,644243,53687,
%T 1288489,3650719,4380863,18917363,3557111,104045497,416181989,
%U 2393046437,455818369,23930464373,47860928747,10255913303,11044829711
%N Numerators of partial sums of reciprocals of lcm(1..n) = A003418(n).
%F a(n) = numerator(Sum_{j=1..n} 1/lcm(1..n)).
%e n = 7: LCM values: 1, 2, 6, 12, 60, 60, 420; partial sum = 1 + 1/2 + 1/6 + 1/12 + 1/60 + 1/60 + 1/420 = (420 + 210 + 70 + 35 + 7 + 7 + 1)/420 = 750/420 = 25/14, so a(7) = 25.
%t q[x_] := Apply[LCM, Table[j, {j, 1, x}]] Table[Numerator[Apply[Plus, Table[1/q[w], {w, 1, m}]]], {m, 1, 30}]
%t Accumulate[Table[1/LCM@@Range[n],{n,30}]]//Numerator (* _Harvey P. Dale_, Aug 08 2021 *)
%Y Cf. A003418, A064858, A064859.
%K nonn,frac
%O 1,2
%A _Labos Elemer_, Oct 08 2001
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