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Number of distinct prime divisors of 2^(2^n)-1 (A051179).
0

%I #7 Dec 15 2017 17:35:22

%S 0,1,2,3,4,5,7,9,11,13,16,20,25

%N Number of distinct prime divisors of 2^(2^n)-1 (A051179).

%C 2^(2^n)-1 is the product of the first n Fermat numbers F(0),...,F(n-1) (A000215). Hence this sequence is just the summation of A046052, which gives the number of prime factors in each Fermat number. - _T. D. Noe_, Jan 07 2003

%D D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, p. 238.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>

%o (PARI) for(n=0,22,print(omega(2^(2^n)-1)))

%Y Cf. A051179, A000215, A046052.

%K nonn

%O 0,3

%A _Jason Earls_, Jul 28 2001

%E More terms from _T. D. Noe_, Jan 07 2003