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 A046800 Number of distinct prime factors of 2^n-1. 19
 0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 4, 1, 3, 3, 4, 1, 4, 1, 5, 3, 4, 2, 6, 3, 3, 3, 6, 3, 6, 1, 5, 4, 3, 4, 8, 2, 3, 4, 7, 2, 6, 3, 7, 6, 4, 3, 9, 2, 7, 5, 7, 3, 6, 6, 8, 4, 6, 2, 11, 1, 3, 6, 7, 3, 8, 2, 7, 4, 9, 3, 12, 3, 5, 7, 7, 4, 7, 3, 9, 6, 5, 2, 12, 3, 5, 6, 10, 1, 11, 5, 9, 3, 6, 5, 12, 2, 5, 8, 12, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Amiram Eldar, Table of n, a(n) for n = 0..1206 (terms 1..500 from T. D. Noe) J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002. AbĂ­lio Lemos and Ady Cambraia Junior, On the number of prime factors of Mersenne numbers (2016) FORMULA a(n) = sum{d|n} A086251(d), Mobius transform of A086251. a(n) < 0.7 * n; the constant 0.7 cannot be improved below log 2 using only the size of 2^n-1. - Charles R Greathouse IV, Apr 12 2012 a(n) = A001221(2^n-1). - R. J. Mathar, Nov 10 2017 EXAMPLE a(6) = 2 because 63 = 3*3*7 has 2 distinct prime factors. MAPLE A046800 := proc(n)     if n <= 1 then         0;     else         numtheory[factorset](2^n-1) ;         nops(%) ;     end if; end proc: seq(A046800(n), n=0..100) ; # R. J. Mathar, Nov 10 2017 MATHEMATICA Table[Length[ FactorInteger [ 2^n -1 ] ], {n, 0, 100}] Join[{0}, PrimeNu/@(2^Range[110]-1)] (* Harvey P. Dale, Mar 09 2015 *) PROG (PARI) a(n)=omega(2^n-1) \\ Charles R Greathouse IV, Nov 17 2014 CROSSREFS Length of row n of A060443. Cf. A000225, A046051 (number of prime factors, with repetition, of 2^n-1), A086251. Sequence in context: A191372 A185316 A053279 * A027350 A029327 A079135 Adjacent sequences:  A046797 A046798 A046799 * A046801 A046802 A046803 KEYWORD nonn AUTHOR EXTENSIONS Edited by T. D. Noe, Jul 14 2003 STATUS approved

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Last modified October 18 14:04 EDT 2019. Contains 328161 sequences. (Running on oeis4.)