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.
Abílio Lemos and Ady Cambraia Junior, On the number of prime factors of Mersenne numbers (2016)
FORMULA
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by T. D. Noe, Jul 14 2003
STATUS
approved