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A090332
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Numbers with no divisors >1 that are prefixes of other divisors in binary representation.
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7
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1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 125, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181
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OFFSET
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1,2
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COMMENTS
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Divisors >1 of a(n) in binary representation form a prefix code.
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LINKS
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FORMULA
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EXAMPLE
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Divisors >1 of a(188)=637: {7,13,49,91,637}, in binary: {111, 1101, 110001, 1011011, 1001111101}.
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MAPLE
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filter:= proc(n) local d, i, j;
d:= numtheory:-divisors(n);
for i in d do
for j from 1 to ilog2(i)-1 do
if member(floor(i/2^j), d) then return false fi
od od;
true
end proc:
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MATHEMATICA
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filterQ[n_] := Catch@Module[{d = Divisors[n], j}, Do[
For[j = 1, j <= Floor@Log[2, i]-1, j++,
If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}];
True];
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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