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A141092 Product of first k composite numbers divided by their sum, when the result is an integer. 12
1, 64, 46080, 111974400, 662171811840, 310393036800000, 7230916185292800, 108238138194410864640000, 23835710455777670400935290994688000000000, 1104077556971139123493322971152384000000000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 27 07:55 EDT 2017. Contains 288777 sequences.