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%I #5 Jul 05 2021 02:36:27
%S 1,5,9,1,8,7,4,1,2,1,9,3,0,1,2,5,0,1,1,2,4,1,6,2,9,5,9,8,0,9,2,1,6,0,
%T 8,5,9,0,8,5,6,6,8,4,2,8,5,8,4,6,4,7,3,3,5,0,6,4,8,9,9,4,7,9,7,0,0,0,
%U 9,8,4,6,3,5,8,4,2,5,7,4,4,2,2,3,0,5,2,2,4,2,3,4,5,3,0,7,9,9,7,2
%N Decimal expansion of Sum_{k>=0} 1/A138534(k).
%C This constant is irrational (Mingarelli, 2013).
%H Angelo B. Mingarelli, <a href="http://nntdm.net/volume-19-2013/number-4/43-76/">Abstract factorials</a>, Notes on Number Theory and Discrete Mathematics, Vol. 19, No. 4 (2013), pp. 43-76 (see p. 62); <a href="https://arxiv.org/abs/0705.4299">arXiv preprint</a>, arXiv:0705.4299 [math.NT], 2007-2012.
%e 1.59187412193012501124162959809216085908566842858464...
%t RealDigits[Sum[1/Product[Prime[k]^Floor[n/k], {k, 1, n}], {n, 0, 50}], 10, 100][[1]]
%Y Cf. A138534, A161360.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, Jul 02 2021