A091336 - OEIS

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

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OFFSET

0,3

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

Table of n, a(n) for n=0..11.

Jens Kruse Andersen, Factorization of Sylvester's sequence

Eric Weisstein's World of Mathematics, Sylvester's sequence

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A000058, A091335.

Sequence in context: A074885 A215231 A301512 * A002235 A217132 A239014

Adjacent sequences: A091333 A091334 A091335 * A091337 A091338 A091339

KEYWORD

hard,more,nonn

AUTHOR

Max Alekseyev, Dec 30 2003

EXTENSIONS

One more term from Max Alekseyev, Sep 11 2006

STATUS

approved