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Number of prime divisors of A000058(n)-1 = A000058(0)*...*A000058(n-1).
3

%I #19 May 09 2017 22:39:50

%S 0,1,2,3,4,6,7,11,15,18,23,27

%N Number of prime divisors of A000058(n)-1 = A000058(0)*...*A000058(n-1).

%C All numbers less than 2.5*10^15 in Sylvester's sequence are squarefree and no squareful numbers in this sequence are known (Vardi 1991).

%D Vardi, I. "Are All Euclid Numbers Squarefree?" and "PowerMod to the Rescue." Sections 5.1 and 5.2 in Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 82-89, 1991.

%H Jens Kruse Andersen, <a href="http://primerecords.dk/sylvester-factors.htm">Factorization of Sylvester's sequence</a>

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

%F a(n) = A001221(A000058(n)-1) = A001221(A000058(0)*...*A000058(n-1)) = Sum_{i=0..(n-1)} A091335(i).

%t PrimeNu[NestList[#^2 - # + 1 &, 2, 10] - 1] (* _G. C. Greubel_, May 09 2017 *)

%Y Cf. A000058, A091335.

%K hard,more,nonn

%O 0,3

%A _Max Alekseyev_, Dec 30 2003

%E One more term from _Max Alekseyev_, Sep 11 2006