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%I #15 May 11 2024 16:16:11
%S 1,4,3,25,1225,29645,715715,206841635,14933966047,718188003533,
%T 86285158710179,82920037520482019,5974606913975783369,
%U 10043314222393291843289,1688189817927745147112851,162139622078364740433577733,35034630647548196605993834769
%N Numerator of Product{prime(k)^2/(prime(k)^2 - 1) | 0<k<=n}, Denominator: A072045.
%C a(n)/A072045(n) -> (Pi^2)/6 (Leonhard Euler, 1748).
%D M. Sigg: "Pi" p. 191 in Lexikon der Mathematik, Band 4, Spektrum Verlag, 2002.
%e For the first 3 primes: 2,3,5: (2^2/(2^2-1))*(3^2/(3^2-1))*(5^2/(5^2-1)) = (4/3)*(9/8)*(25/24) = (4*9*25)/(3*8*24) = 25/16, therefore a(3)=25;
%e a(10)/A072045(10)=86285158710179/52836150804480=1.63307049.
%t Numerator/@Rest[FoldList[Times,1,#/(#-1)&/@(Prime[Range[15]]^2)]] (* _Harvey P. Dale_, May 03 2011 *)
%Y Cf. A000040, A001248, A236435, A236436.
%K nonn,frac
%O 0,2
%A _Reinhard Zumkeller_, Jun 09 2002
%E a(0)=1 prepended by _Alois P. Heinz_, May 11 2024