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

1,2

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.

Links

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

Formula

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A196415, A141089, A141090, A141091.

Compare with A140761, A159578, A140763, A116536.

Cf. A116536.

Sequence in context: A098843 A159400 A221615 * A283924 A016830 A249076

Adjacent sequences: A141089 A141090 A141091 * A141093 A141094 A141095

Keyword

easy,nonn

Author

Enoch Haga, Jun 01 2008

Extensions

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

Status

approved