A091336 Number of prime divisors of A000058(n)-1 = A000058(0)*...*A000058(n-1).

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

Offset: 0

Author

Max Alekseyev, Dec 30 2003

Keywords

• hard
• more
• nonn

Comments

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).

References

• 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.

Links

• Jens Kruse Andersen, Factorization of Sylvester's sequence
• Eric Weisstein's World of Mathematics, Sylvester's sequence

Crossrefs

Cf. A000058, A091335.

Programs

Mathematica

PrimeNu[NestList[#^2 - # + 1 &, 2, 10] - 1] (* G. C. Greubel, May 09 2017 *)

Formula

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

Extensions

One more term from Max Alekseyev, Sep 11 2006