A111928 Numerator of f(n) := Product_{i=1..n} sigma(i)/i.

1, 3, 2, 7, 21, 42, 48, 18, 26, 234, 2808, 6552, 7056, 12096, 96768, 187488, 3374784, 7312032, 29248128, 307105344, 467970048, 8423460864, 202163060736, 101081530368, 3133527441408, 5061852020736, 1499808006144, 2999616012288, 17997696073728, 215972352884736

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

Harvey P. Dale, Table of n, a(n) for n = 1..808

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_] := Numerator@ Product[ DivisorSigma[1, i]/i, {i, n}]; Array[f, 30] (* Robert G. Wilson v, May 01 2006 *)
Numerator[FoldList[Times, Table[DivisorSigma[1, n]/n, {n, 30}]]] (* Harvey P. Dale, Jan 17 2016 *)

Crossrefs

Cf. A111934.

Sequence in context: A316087 A196537 A173099 * A348695 A248054 A329421

Adjacent sequences: A111925 A111926 A111927 * A111929 A111930 A111931

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 27 2005

Status

approved