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Product of first k composite numbers divided by their sum, when the result is an integer.
14

%I #25 Jan 14 2015 15:48:37

%S 1,64,46080,111974400,662171811840,310393036800000,7230916185292800,

%T 108238138194410864640000,23835710455777670400935290994688000000000,

%U 1104077556971139123493322971152384000000000

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

%C 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.

%H Reinhard Zumkeller, <a href="/A141092/b141092.txt">Table of n, a(n) for n = 1..90</a>

%F a(n) = A036691(A196415(n)) / A053767(A196415(n)). [_Reinhard Zumkeller_, Oct 03 2011]

%e 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.

%t 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 *)

%o (Haskell)

%o import Data.Maybe (catMaybes)

%o a141092 n = a141092_list !! (n-1)

%o a141092_list = catMaybes $ zipWith div' a036691_list a053767_list where

%o div' x y | m == 0 = Just x'

%o | otherwise = Nothing where (x',m) = divMod x y

%o -- _Reinhard Zumkeller_, Oct 03 2011

%o (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

%Y Cf. A196415, A141089, A141090, A141091.

%Y Compare with A140761, A159578, A140763, A116536.

%Y Cf. A116536.

%K easy,nonn

%O 1,2

%A _Enoch Haga_, Jun 01 2008

%E Checked by _N. J. A. Sloane_, Oct 02 2011.