A178110 Consider the set of divisors d of binomial(n-d-1,d-1) where gcd(n,d)>1 and 1

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

Offset: 1

Author

Vladimir Shevelev, May 20 2010

Keywords

• nonn

Examples

			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.
		

Links

• V. Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Int. J. Number Theory, 3 (1) (2007), 119-139.

Crossrefs

Cf. A138389, A178071, A178098, A178099, A178100, A178101, A178105, A178109.

Programs

Maple

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

Mathematica

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 *)

Extensions

39 removed and 82 added by R. J. Mathar, Aug 20 2010

More terms from Amiram Eldar, Jan 20 2019