A141092 Product of first k composite numbers divided by their sum, when the result is an integer.

1, 64, 46080, 111974400, 662171811840, 310393036800000, 7230916185292800, 108238138194410864640000, 23835710455777670400935290994688000000000, 1104077556971139123493322971152384000000000

Offset: 1

Author

Enoch Haga, Jun 01 2008

Keywords

• easy
• nonn

Comments

Find the products and sums of first k composites, k = 1, 2, 3, .... When the products divided by the sums produce integral quotients, add terms to sequence.

Examples

			a(3)=46080 because 4*6*8*9*10*12*14=2903040 and 4+6+8+9+10+12+14=63; 2903040/63=46080, which is an integer, so 46080 is a term.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..90

Crossrefs

Cf. A196415, A141089, A141090, A141091.

Compare with A140761, A159578, A140763, A116536.

Cf. A116536.

Programs

Haskell

import Data.Maybe (catMaybes)
a141092 n = a141092_list !! (n-1)
a141092_list = catMaybes $ zipWith div' a036691_list a053767_list where
   div' x y | m == 0    = Just x'
            | otherwise = Nothing where (x',m) = divMod x y
-- Reinhard Zumkeller, Oct 03 2011

Mathematica

With[{cnos=Select[Range[50],CompositeQ]},Select[Table[Fold[ Times,1,Take[ cnos,n]]/ Total[Take[cnos,n]],{n,Length[cnos]}],IntegerQ]] (* Harvey P. Dale, Jan 14 2015 *)

PARI

s=0;p=1;forcomposite(n=4,100,p*=n;s+=n;if(p%s==0,print1(p/s", "))) \\ Charles R Greathouse IV, Apr 04 2013

Formula

a(n) = A036691(A196415(n)) / A053767(A196415(n)). [Reinhard Zumkeller, Oct 03 2011]

Extensions

Checked by N. J. A. Sloane, Oct 02 2011.