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 A099477 Numbers having no divisors d such that also d+2 is a divisor. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 18 19:19 EDT 2020. Contains 337172 sequences. (Running on oeis4.)