A111928 - OEIS

%I #14 Jan 17 2016 12:47:42

%S 1,3,2,7,21,42,48,18,26,234,2808,6552,7056,12096,96768,187488,3374784,

%T 7312032,29248128,307105344,467970048,8423460864,202163060736,

%U 101081530368,3133527441408,5061852020736,1499808006144,2999616012288,17997696073728,215972352884736

%N Numerator 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.

%H Harvey P. Dale, <a href="/A111928/b111928.txt">Table of n, a(n) for n = 1..808</a>

%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_] := Numerator@ Product[ DivisorSigma[1, i]/i, {i, n}]; Array[f, 30] (* _Robert G. Wilson v_, May 01 2006 *)

%t Numerator[FoldList[Times,Table[DivisorSigma[1,n]/n,{n,30}]]] (* _Harvey P. Dale_, Jan 17 2016 *)

%Y Cf. A111934.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Nov 27 2005