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Search: id:A091335
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| A091335 |
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Number of prime divisors of n-th term of Sylvester's sequence A000058. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 4, 4, 3, 5, 4
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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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).
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Sylvester's sequence
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FORMULA
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a(n)=A001221(A000058(n)).
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000058, A014546, A091336.
Sequence in context: A095830 A101621 A086484 this_sequence A140946 A008741 A110316
Adjacent sequences: A091332 A091333 A091334 this_sequence A091336 A091337 A091338
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KEYWORD
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hard,nonn
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), Dec 30 2003
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EXTENSIONS
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a(9) from T. D. Noe (noe(AT)sspectra.com), Dec 31 2003
a(10) from Ken Takusagawa (kenta(AT)cs.stanford.edu), Apr 11 2006
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