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%I #70 Jul 25 2023 19:56:07
%S 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,
%T 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,
%U 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
%N Number of prime factors of 2^n + 1 (counted with multiplicity).
%C The length of row n in A001269.
%H <a href="/A054992/b054992.txt">Table of n, a(n) for n = 1..1122</a>
%H S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F a(n) = A046051(2n) - A046051(n). - _T. D. Noe_, Jun 18 2003
%F a(n) = A001222(A000051(n)). - _Amiram Eldar_, Oct 04 2019
%e a(3) = 2 because 2^3 + 1 = 9 = 3*3.
%t a[q_] := Module[{x, n}, x=FactorInteger[2^n+1]; n=Length[x]; Sum[Table[x[i]][2]], {i, n}][j]], {j, n}]]
%t A054992[n_Integer] := PrimeOmega[2^n + 1]; Table[A054992[n], {n,200}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2011 *)
%o (PARI) a(n)=bigomega(2^n+1) \\ _Charles R Greathouse IV_, Apr 29 2015
%Y bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), this sequence (b=2).
%Y Cf. A000051, A002586, A002587, A003260, A001222, A001269, A001348, A054988, A054989, A054990, A054991, A000978.
%Y Cf. A046051 (number of prime factors of 2^n-1).
%Y Cf. A086257 (number of primitive prime factors).
%K nonn
%O 1,3
%A Arne Ring (arne.ring(AT)epost.de), May 30 2000
%E Extended by _Patrick De Geest_, Oct 01 2000
%E Terms to a(500) in b-file from _T. D. Noe_, Nov 10 2007
%E Deleted duplicate (and broken) Wagstaff link. - _N. J. A. Sloane_, Jan 18 2019
%E a(500)-a(1062) in b-file from _Amiram Eldar_, Oct 04 2019
%E a(1063)-a(1122) in b-file from _Max Alekseyev_, Jul 15 2023
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