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

1,2

Comments

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

Links

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

Formula

A099475(a(n)) = 0.

Example

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.

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 *)

Crossrefs

Complement of A059267.

Cf. A099475, A108118.

Sequence in context: A142879 A284167 A108118 * A261034 A330777 A259749

Adjacent sequences: A099474 A099475 A099476 * A099478 A099479 A099480

Keyword

nonn

Author

Reinhard Zumkeller, Oct 18 2004

Status

approved