A196415 Values of n such that (product of first n composite numbers) / (sum of first n composite numbers) is an integer.

1, 4, 7, 10, 13, 15, 16, 21, 32, 33, 56, 57, 60, 70, 77, 80, 83, 84, 88, 92, 93, 97, 112, 114, 115, 120, 122, 130, 134, 141, 147, 153, 155, 164, 165, 188, 191, 196, 201, 202, 213, 222, 225, 226, 229, 243, 245, 248, 252, 260, 264, 265, 268, 273, 274, 281

Offset

1,2

Comments

A036691(a(n)) mod A053767(a(n)) = 0, A141092(n) = A036691(a(n)) / A053767(a(n)). [Reinhard Zumkeller, Oct 03 2011]

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Maple

# First define list of composite numbers:
tc:=[4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27,
28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49,
50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69,
70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88];
a1:=n->mul(tc[i], i=1..n);
a2:=n->add(tc[i], i=1..n);
sn:=[];
s0:=[];
s1:=[];
s2:=[];
for n from 1 to 40 do
  t1:=a1(n)/a2(n);
  if whattype(t1) = integer then
   sn:= [op(sn), n];
   s0:= [op(s0), t1];
   s1:= [op(s1), a1(n)];
   s2:= [op(s2), a2(n)];
fi;
od:
sn; s0; s1; s2;
# alternatively
for n from 1 to 1000 do
        if type(A036691(n)/A053767(n), 'integer') then
                printf("%d, ", n);
        end if;
end do: # R. J. Mathar, Oct 03 2011

Mathematica

c = Select[Range[2, 355], ! PrimeQ@# &]; p = 1; s = 0; Select[Range@ Length@c, Mod[p *= c[[#]], s += c[[#]]] == 0 &] (* Giovanni Resta, Apr 03 2013 *)

Prog

(Haskell)
import Data.List (elemIndices)
a196415 n = a196415_list !! (n-1)
a196415_list =
   map (+ 1) $ elemIndices 0 $ zipWith mod a036691_list a053767_list
-- Reinhard Zumkeller, Oct 03 2011

Crossrefs

Cf. A051838, A141090, A141091, A141092.

Sequence in context: A327422 A260165 A055054 * A186327 A190362 A184904

Adjacent sequences: A196412 A196413 A196414 * A196416 A196417 A196418

Keyword

nonn

Author

N. J. A. Sloane, Oct 02 2011

Extensions

More terms from Arkadiusz Wesolowski, Oct 03 2011

Status

approved