A111934 Denominator of f(n) := Product_{i=1..n} sigma(i)/i.

1, 2, 1, 2, 5, 5, 5, 1, 1, 5, 55, 55, 55, 55, 275, 275, 4675, 4675, 17765, 88825, 88825, 977075, 22472725, 4494545, 112363625, 112363625, 22472725, 22472725, 130341805, 651709025, 651709025, 651709025, 7168799275, 121869587675, 609347938375, 609347938375

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..36.

Example

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, ...

Maple

with(numtheory); f:=n->mul(sigma(i)/i, i=1..n);

Mathematica

f[n_] := Denominator@ Product[ DivisorSigma[1, i]/i, {i, n}]; Array[f, 36] (* Robert G. Wilson v, May 01 2006 *)
Denominator[Rest[FoldList[Times, 1, Table[DivisorSigma[1, i]/i, {i, 40}]]]] (* Harvey P. Dale, Nov 12 2014 *)

Crossrefs

Cf. A111928.

Sequence in context: A241138 A241349 A330405 * A098509 A019910 A084309

Adjacent sequences: A111931 A111932 A111933 * A111935 A111936 A111937

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 27 2005

Status

approved