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%I #21 Nov 17 2020 11:04:52
%S 1,6,9,1,7,9,9,2,0,9,8,2,1,7,1,2,3,5,1,3,3,9,2,6,1,8,0,6,7,8,7,6,3,1,
%T 8,6,9,8,2,3,6,9,3,7,6,2,9,2,5,8,1,9,1,3,4,5,5,6,9,5,2,0,1,4,3,4,9,2,
%U 5,7,2,0,9,1,1,5,8,3,4,5,7,1,3,0,3,9,8,3,5,9,7,3,2,5,0,1,7,7,8,0,0,2,5,3,9
%N Decimal expansion of Sum_{i>=1} 1/A092143(i).
%C It follows from the Mingarelli reference that this number is irrational.
%H Angelo B. Mingarelli, <a href="http://arXiv.org/abs/0705.4299">Abstract factorials of arbitrary sets of integers</a>, arXiv:0705.4299 [math.NT], 200-2012.
%e 1.6917992098217123513392618067876318698236937629258191345569...
%p Digits := 60 : A092143 := proc(n) option remember ; local dvs ; if n = 1 then 1 ; else dvs := numtheory[divisors](n) ; A092143(n-1)*mul(i,i=dvs) ; fi ; end: A129635 := proc(isum) a := 0.0 ; for i from 1 to isum do a := a+1.0/A092143(i) ; print(evalf(a)) ; od ; RETURN(a) ; end: A129635(200) ; # _R. J. Mathar_, Sep 02 2007
%t digits = 105; A092143[m_] := For[n = k = 1, k <= m, k++, Do[n = n*d, {d, Divisors[k]}]; If[k == m, Return[n]]] ;rd[j_] := rd[j] = RealDigits[ N[ Sum[ 1/A092143[m], {m, 1, 2^j}], digits]][[1]]; rd[j = 4]; While[ rd[j] != rd[j - 1], j++]; rd[j] (* _Jean-François Alcover_, Oct 30 2012 *)
%Y Cf. A092143.
%K cons,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, May 31 2007
%E More terms from _R. J. Mathar_, Sep 02 2007
%E Edited by _N. J. A. Sloane_, Sep 16 2007 and May 06 2008
%E More digits from _R. J. Mathar_, Jul 12 2009
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