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A054992 Number of prime factors of 2^n + 1 (counted with multiplicity). 21
1, 1, 2, 1, 2, 2, 2, 1, 4, 3, 2, 2, 2, 3, 4, 1, 2, 4, 2, 2, 4, 3, 2, 3, 4, 4, 6, 2, 3, 6, 2, 2, 5, 4, 5, 4, 3, 4, 4, 2, 3, 6, 2, 3, 7, 5, 3, 3, 3, 7, 6, 3, 3, 6, 6, 3, 5, 3, 4, 4, 2, 5, 7, 2, 6, 6, 3, 4, 5, 7, 3, 5, 3, 5, 7, 4, 6, 10, 2, 3, 10, 5, 6, 5, 4, 5, 5, 4, 4, 11, 6, 2, 5, 4, 5, 3, 5, 6, 9, 6, 2, 9, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The length of row n in A001269.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1062 (terms 0..500 from T. D. Noe)

S. S. Wagstaff, Jr., The Cunningham Project

FORMULA

a(n) = A046051(2n) - A046051(n). - T. D. Noe, Jun 18 2003

a(n) = A001222(A000051(n)). - Amiram Eldar, Oct 04 2019

EXAMPLE

a(3) = 2 because 2^3 + 1 = 9 = 3*3.

MATHEMATICA

a[q_] := Module[{x, n}, x=FactorInteger[2^n+1]; n=Length[x]; Sum[Table[x[i]][2]], {i, n}][j]], {j, n}]]

A054992[n_Integer] := PrimeOmega[2^n + 1]; Table[A054992[n], {n, 200}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

PROG

(PARI) a(n)=bigomega(2^n+1) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A000051, A002586, A002587, A003260, A001222, A001269, A001348, A054988, A054989, A054990, A054991, A057934-A057941, A000978.

Cf. A046051 (number of prime factors of 2^n-1).

Cf. A086257 (number of primitive prime factors).

Sequence in context: A016727 A241318 A276064 * A096495 A276062 A324386

Adjacent sequences:  A054989 A054990 A054991 * A054993 A054994 A054995

KEYWORD

nonn

AUTHOR

Arne Ring (arne.ring(AT)epost.de), May 30 2000

EXTENSIONS

Extended by Patrick De Geest, Oct 01 2000

Deleted duplicate (and broken) Wagstaff link. - N. J. A. Sloane, Jan 18 2019

STATUS

approved

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)