A091335 Number of prime divisors of n-th term of Sylvester's sequence A000058.

1, 1, 1, 1, 2, 1, 4, 4, 3, 5, 4

Offset

0,5

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).

a(n) is currently unknown for all n > 10. - Jens Kruse Andersen, Jun 19 2014

References

Ilan Vardi, "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..10.

Jens Kruse Andersen, Factorization of Sylvester's sequence

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

Formula

a(n) = A001221(A000058(n)).

Example

a(8) = 3 because A000058(8) = 5295435634831 * 31401519357481261 * 77366930214021991992277 is a product of 3 primes.
a(9) = 5 because A000058(9) = 181 * 1987 * 112374829138729 * 114152531605972711 * 35874380272246624152764569191134894955972560447869169859142453622851 is the product of 5 prime factors
a(10) = 4 because A000058(10) = 2287 * 2271427 * 21430986826194127130578627950810640891005487 * P156 is the product of 4 prime factors.
Here P156 = 24605022397522123277426691306421099608611770732459695261246331125\
73460100430857224101455594897691626456909430029315374035313628946949460093682\
49974883220589.

Mathematica

PrimeNu[NestList[#^2 - # + 1 &, 2, 7]] (* G. C. Greubel, May 09 2017 *)

Crossrefs

Cf. A000058, A001221, A014546, A091336.

Sequence in context: A086484 A349572 A349571 * A362865 A274883 A140946

Adjacent sequences: A091332 A091333 A091334 * A091336 A091337 A091338

Keyword

hard,more,nonn

Author

Max Alekseyev, Dec 30 2003

Extensions

a(9) from T. D. Noe, Dec 31 2003

a(10) from Ken Takusagawa, Apr 11 2006

Status

approved