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 A102469 Largest prime factor of numerator of Sum_{k=0...n} 1/k!, with a(0) = 1. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). REFERENCES J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641. LINKS 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 FORMULA A006530(A061354(n)). EXAMPLE Sum_{k=0...3} 1/k! = 8/3 and 2 is the largest prime factor 8, so a(3) = 2. MATHEMATICA FactorInteger[#][[-1, 1]]&/@Numerator[Accumulate[1/Range[0, 30]!]] (* Harvey P. Dale, Nov 14 2012 *) CROSSREFS Cf. A102468, A096058, A006530, A061354, A000522, A007917. Sequence in context: A205715 A181338 A211175 * A098886 A089120 A019295 Adjacent sequences:  A102466 A102467 A102468 * A102470 A102471 A102472 KEYWORD nonn AUTHOR Jonathan Sondow, Jan 09 2005 STATUS approved

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