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%I #13 Jan 20 2019 06:19:09
%S 16,18,26,27,32,34,40,45,50,56,58,63,64,72,74,80,81,82,88,90,98,99,
%T 104,106,112,117,122,128,130,135,136,144,146,152,153,154,160,162,170,
%U 171,176,178,184,189,194,200,202,207,208,216,218,224,225,226,232,234,242
%N 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.
%H V. Shevelev, <a href="http://dx.doi.org/10.1142/S179304210700078X">On divisibility of binomial(n-i-1,i-1) by i</a>, Int. J. Number Theory, 3 (1) (2007), 119-139.
%e The set for n =14 is {4}, which does not admit 14 into the sequence.
%e The set for n =16 is {6}, which adds 16 to the sequence.
%e The set for n = 38 is {4,12,14}, which does not admit 38 into the sequence.
%p 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:
%p for n from 1 to 100 do if isA178110(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Aug 20 2010
%t 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 *)
%Y Cf. A138389, A178071, A178098, A178099, A178100, A178101, A178105, A178109.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, May 20 2010
%E 39 removed and 82 added by _R. J. Mathar_, Aug 20 2010
%E More terms from _Amiram Eldar_, Jan 20 2019
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