A046799 Number of distinct prime factors of 2^n+1.

1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 1, 2, 4, 2, 2, 3, 3, 2, 3, 4, 4, 3, 2, 3, 5, 2, 2, 4, 4, 5, 4, 3, 4, 3, 2, 3, 6, 2, 3, 5, 5, 3, 3, 3, 5, 5, 3, 3, 6, 5, 3, 4, 3, 4, 4, 2, 5, 5, 2, 6, 6, 3, 3, 4, 6, 3, 5, 3, 5, 6, 4, 6, 9, 2, 3, 6, 5, 6, 5, 4, 5, 4, 4, 4, 10, 6, 2, 4, 4, 5, 3, 5, 6, 7, 6, 2, 9, 3, 2

Offset

0,6

Comments

The length of row n in A060444.

Links

Max Alekseyev, Table of n, a(n) for n = 0..1122 (terms 0..500 from T. D. Noe; terms 501..1062 from Amiram Eldar)

Formula

a(n) = A001221(A000051(n)). - Amiram Eldar, Oct 04 2019

Example

For n=7, 129 = 3.43 has 2 prime factors, so a(7) = 2.

Mathematica

PrimeNu[1 + 2^#] & /@ Range[0, 104] (* Jayanta Basu, Jun 29 2013 *)

Prog

(PARI) a(n) = omega(2^n+1); \\ Michel Marcus, Mar 25 2017

Crossrefs

Cf. A000051, A001221, A060444, A086257 (number of primitive prime factors).

Sequence in context: A032539 A122922 A278570 * A348172 A319506 A037809

Adjacent sequences: A046796 A046797 A046798 * A046800 A046801 A046802

Keyword

nonn

Author

Labos Elemer

Status

approved