A178110 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.

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

1,1

Links

Table of n, a(n) for n=1..57.

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A255847 A160778 A057369 * A117100 A101848 A032401

Adjacent sequences: A178107 A178108 A178109 * A178111 A178112 A178113

Keyword

nonn

Author

Vladimir Shevelev, May 20 2010

Extensions

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

More terms from Amiram Eldar, Jan 20 2019

Status

approved