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A196415 Values of n such that (product of first n composite numbers) / (sum of first n composite numbers) is an integer. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A090384 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

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Last modified May 29 12:59 EDT 2017. Contains 287247 sequences.