A099477 Numbers having no divisors d such that also d+2 is a divisor.

1, 2, 5, 7, 10, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 49, 50, 53, 55, 58, 59, 61, 62, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 86, 89, 91, 94, 95, 97, 98, 101, 103, 106, 107, 109, 110, 113, 115, 118, 119, 121, 122, 125, 127, 130, 131, 133

Offset: 1

Author

Reinhard Zumkeller, Oct 18 2004

Keywords

• nonn

Comments

Except for 3, all primes are in this sequence. - Alonso del Arte, Jun 13 2014

Examples

			10 is in the sequence because its divisors are 1, 2, 5, 10, none of which is 2 less than another.
11 is in the sequence as are all primes other than 3.
12 is not in the sequence because its divisors are 1, 2, 3, 4, 6, 12, of which 2 and 4 are 2 less than another divisor.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A059267.

Cf. A099475, A108118.

Programs

Mathematica

twinDivsQ[n_] := Union[ IntegerQ[ # ] & /@ (n/(Divisors[n] + 2))][[ -1]] == True; Select[ Range[133], !twinDivsQ[ # ] &] (* Robert G. Wilson v, Jun 09 2005 *)
d2noQ[n_]:=Module[{d=Divisors[n]},Intersection[d,d+2]=={}]; Select[ Range[ 150],d2noQ] (* Harvey P. Dale, Feb 15 2019 *)

Formula

A099475(a(n)) = 0.