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A102469
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Largest prime factor of numerator of Sum_{k=0...n} 1/k!, with a(0) = 1.
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1
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1, 2, 5, 2, 13, 163, 103, 137, 863, 98641, 10687, 31469, 1540901, 522787, 5441, 226871807, 13619, 1276861, 414026539, 2124467, 12670743557, 838025081381, 44659157, 323895443, 337310723185584470837549, 54352957
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OFFSET
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0,2
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COMMENTS
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It appears that a(n) = A102468(n) (Smarandache number of the same numerator) except when n = 3. The largest prime factor of the corresponding denominator is A007917(n) for n > 1. Omitting the 0-th term in the sum, it appears that the largest prime factor and the Smarandache number, of the numerator of Sum_{k=1...n} 1/k! are both equal to A096058(n).
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REFERENCES
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J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
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Table of n, a(n) for n=0..25.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.
Eric Weisstein's World of Mathematics, GreatestPrimeFactor
Index entries for sequences related to factorial numbers.
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FORMULA
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A006530(A061354(n)).
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EXAMPLE
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Sum_{k=0...3} 1/k! = 8/3 and 2 is the largest prime factor 8, so a(3) = 2.
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MATHEMATICA
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FactorInteger[#][[-1, 1]]&/@Numerator[Accumulate[1/Range[0, 30]!]] (* Harvey P. Dale, Nov 14 2012 *)
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CROSSREFS
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Cf. A102468, A096058, A006530, A061354, A000522, A007917.
Sequence in context: A205715 A181338 A211175 * A098886 A089120 A019295
Adjacent sequences: A102466 A102467 A102468 * A102470 A102471 A102472
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KEYWORD
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nonn
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AUTHOR
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Jonathan Sondow, Jan 09 2005
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STATUS
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approved
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