A067886 Numbers k such that 2^k+1 and 2^k-1 have the same number of distinct prime factors.

2, 3, 6, 9, 11, 14, 15, 18, 21, 23, 27, 29, 33, 42, 47, 51, 53, 54, 57, 69, 71, 73, 74, 81, 82, 86, 95, 101, 105, 111, 113, 114, 115, 121, 129, 130, 138, 141, 142, 165, 167, 169, 179, 181, 199, 203, 209, 213, 230, 233, 235, 243, 250, 255, 258, 277, 279, 306, 307

Offset: 1

Author

Benoit Cloitre, Mar 02 2002

Keywords

• nonn

Comments

Numbers k such that omega(2^k+1) = omega(2^k-1).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..141

Crossrefs

Cf. A001221, A046799, A046800.

Programs

Magma

[k: k in [2..307] | #PrimeDivisors(2^k-1) eq #PrimeDivisors(2^k+1) ]; // Marius A. Burtea, Feb 13 2020

Mathematica

sndpQ[n_]:=Module[{c=2^n},PrimeNu[c+1]==PrimeNu[c-1]]; Select[Range[ 250], sndpQ] (* Harvey P. Dale, Feb 04 2016 *)

PARI

isok(k) = omega(2^k-1) == omega(2^k+1); \\ Michel Marcus, Feb 13 2020

Extensions

More terms from Rick L. Shepherd, May 14 2002

More terms from Amiram Eldar, Feb 13 2020