|
|
A141092
|
|
Product of first k composite numbers divided by their sum, when the result is an integer.
|
|
14
|
|
|
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
|
|
|
FORMULA
|
|
|
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
(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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|