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A196415
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Values of n such that (product of first n composite numbers) / (sum of first n composite numbers) is an integer.
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7
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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MAPLE
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# 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
printf("%d, ", n);
end if;
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a196415 n = a196415_list !! (n-1)
a196415_list =
map (+ 1) $ elemIndices 0 $ zipWith mod a036691_list a053767_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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