This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093101 Cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms. 20
 1, 1, 1, 2, 1, 2, 1, 20, 1, 10, 1, 8, 5, 2, 5, 4, 1, 130, 1, 4000, 1, 2, 5, 52, 5, 494, 1, 40, 1, 10, 13, 4, 25, 38, 5, 16, 13, 230, 13, 20, 1, 46, 5, 104, 475, 62, 1, 20, 1, 130, 31, 832, 2755, 74, 5, 4, 13, 50, 1, 40, 23, 2, 2795, 76, 34385, 2, 1, 80, 1, 650, 1, 2812, 5, 74, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Same as n!/A061355(n) and (1+n+n(n-1)+n(n-1)(n-2)+...+n!)/A061354(n). a(n) is relatively prime to n. gcd(a(n),a(n+1)) = 1. LINKS Antti Karttunen, Table of n, a(n) for n = 0..4096 J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641. J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010. 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. FORMULA a(n) = gcd(n!, 1+n+n(n-1)+n(n-1)(n-2)+...+n!). a(n) = gcd(n!, A(n)) where A(0) = 1, A(n) = n*A(n-1)+1. EXAMPLE E.g. 1/0!+1/1!+1/2!+1/3!=16/6=(2*8)/(2*3) so a(3)=2. MATHEMATICA f[n_] := n! / Denominator[ Sum[1/k!, {k, 0, n}]]; Table[ f[n], {n, 0, 74}] (* Robert G. Wilson v *) (* Second program: *) A[n_] := If[n==0, 1, n*A[n-1]+1]; Table[GCD[A[n], n! ], {n, 0, 74}] PROG (PARI) A000522(n) = sum(k=0, n, binomial(n, k)*k!); \\ This function from Joerg Arndt, Dec 14 2014 A093101(n) = gcd(n!, A000522(n)); \\ Antti Karttunen, Jul 12 2017 CROSSREFS Cf. A093647, A093651. (n+1)!/(a(n)*a(n+1)) = A123899(n). (n+3)!/(a(n)*a(n+1)*a(n+2)) = A123900(n). (n+3)/GCD(a(n), a(n+2)) = A123901(n). Cf. also A000522, A061354, A061355. Sequence in context: A287541 A288196 A072883 * A082469 A206566 A088151 Adjacent sequences:  A093098 A093099 A093100 * A093102 A093103 A093104 KEYWORD nonn AUTHOR Jonathan Sondow, May 10 2004, Oct 18 2006 EXTENSIONS More terms from Robert G. Wilson v, May 14 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 04:46 EDT 2019. Contains 323579 sequences. (Running on oeis4.)