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%I #8 Dec 15 2017 17:35:16
%S 3,24,2,70,1680,55440,55440,65520,65520,5040,10080,5040,1627920,
%T 1627920,85680,942480,21677040,492660,107100,64260,621180,1242360,
%U 1328040,10624320,1328040,14608440,1217370,277560360,133506533160
%N Denominator of sum of first n terms of the series 1/3 + 1/8 + 1/24 ... in which the denominators are one less than a perfect square that cannot otherwise be written as a power (cf. A062757, A037450).
%D W. Dunham, Euler: The Master of Us All, The Mathematical Association of America, Washington D.C., 1999, p. 66.
%D L. Euler, "Variae observationes circa series infinitas," Opera Omnia, Ser. 1, Vol. 14, pp. 216-244.
%H L. Euler, <a href="http://math.dartmouth.edu/~euler/pages/E072.html">Variae observationes circa series infinitas</a>
%t Table[ Denominator[ Plus@@(Take[ Select[ Range[ 2, 50 ], GCD@@(Last/@FactorInteger[ # ])==1& ]^2-1, k ]^-1) ], {k, 1, 29} ]
%Y Cf. A062757, A037450.
%K nonn
%O 1,1
%A _Jason Earls_, Jul 21 2001
%E More terms from _Dean Hickerson_, Jul 24, 2001