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A178110
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Consider the set of divisors d of binomial(n-d-1,d-1) where gcd(n,d)>1 and 1<d<=n/2. If the smallest element of this set is 6, n is in the sequence.
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2
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16, 18, 26, 27, 32, 34, 40, 45, 50, 56, 58, 63, 64, 72, 74, 80, 81, 82, 88, 90, 98, 99, 104, 106, 112, 117, 122, 128, 130, 135, 136, 144, 146, 152, 153, 154, 160, 162, 170, 171, 176, 178, 184, 189, 194, 200, 202, 207, 208, 216, 218, 224, 225, 226, 232, 234, 242
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The set for n =14 is {4}, which does not admit 14 into the sequence.
The set for n =16 is {6}, which adds 16 to the sequence.
The set for n = 38 is {4,12,14}, which does not admit 38 into the sequence.
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MAPLE
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isA178110 := proc(n) local dvs, d ; dvs := {} ; for d from 1 to n/2 do if gcd(n, d) > 1 and d in numtheory[divisors]( binomial(n-d-1, d-1)) then dvs := dvs union {d} ; end if; end do: return (min(op(dvs)) = 6) ; end proc:
for n from 1 to 100 do if isA178110(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Aug 20 2010
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MATHEMATICA
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bQ[n_] := Module[{B={}}, Do[If[GCD[i, n]>1 && Divisible[Binomial[n-i-1, i-1], i], AppendTo[B, i]], {i, 2, Floor[n/2]}]; Min[B]==6]; Select[Range[250], bQ] (* Amiram Eldar, Jan 20 2019 *)
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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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