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%I #12 Feb 16 2015 10:24:00
%S 1,2,1,2,5,5,5,1,1,5,55,55,55,55,275,275,4675,4675,17765,88825,88825,
%T 977075,22472725,4494545,112363625,112363625,22472725,22472725,
%U 130341805,651709025,651709025,651709025,7168799275,121869587675,609347938375,609347938375
%N Denominator of f(n) := Product_{i=1..n} sigma(i)/i.
%C _R. K. Guy_ observes (Nov 23 2005) that it appears that f(n) is an integer iff n = 1, 3, 8, 9, when f(n) = 1, 2, 18, 26 respectively.
%e 1, 3/2, 2, 7/2, 21/5, 42/5, 48/5, 18, 26, 234/5, 2808/55, 6552/55, 7056/55, 12096/55, 96768/275, 187488/275, 3374784/4675, 7312032/4675, 29248128/17765, 307105344/88825, ...
%p with(numtheory); f:=n->mul(sigma(i)/i,i=1..n);
%t f[n_] := Denominator@ Product[ DivisorSigma[1, i]/i, {i, n}]; Array[f, 36] (* _Robert G. Wilson v_, May 01 2006 *)
%t Denominator[Rest[FoldList[Times,1,Table[DivisorSigma[1,i]/i,{i,40}]]]] (* _Harvey P. Dale_, Nov 12 2014 *)
%Y Cf. A111928.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Nov 27 2005
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