0,3

An inverse of the Smarandache function: A002034(a(n)) = n for n > 0. But not the least inverse: a(n) > A046021(n) for n > 3. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 09 2005

Contribution from Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 03 2008: (Start)

Furdui proves that, if e_n = (1+(1/n))^n then

Limit[n->infinity] n*((e_n)^e - e^(A061354(n)/A061355(n)) = -(1/2)*e^(e+1). (End)

J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.

Ovidiu Furdui, solution to problem 91.H, Mathematical Gazette, Vol. 92, No. 523, March 2008, 174-175. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 03 2008]

Harry J. Smith, Table of n, a(n) for n=0,...,200

Index entries for sequences related to factorial numbers.

Denominators of floor(n!*exp(1))/n!. Denominators of coefficients in expansion of exp(x)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 11 2002

n!/GCD(n!, 1+n+n(n-1)+n(n-1)(n-2)+...+n!) - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 09 2005

1, 2, 5/2, 8/3, 65/24, 163/60, 1957/720, 685/252, ...

BB:=n->sum(1/i!, i=1..n): a:=n->floor(denom(BB(n))): seq(a(n), n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2007

(PARI) { default(realprecision, 500); e=exp(1); for (n=0, 200, a=denominator(floor(n!*e)/n!); write("b061355.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 21 2009]

Cf. A061354, A093101.

a(n) = n!/A093101(n) for n > 0. See also A002034, A046021.

Sequence in context: A092049 A061778 A118204 this_sequence A057665 A157327 A009231

Adjacent sequences: A061352 A061353 A061354 this_sequence A061356 A061357 A061358

nonn,frac

Amarnath_murthy (amarnath_murthy(AT)yahoo.com), Apr 28 2001