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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 February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)