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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.
2
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
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 *)
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